لﻭﻷﺍ ﻥﻴﺭﻤﺘﻟﺍ لﺤ):4ﻥ( 1

ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ لﺤﻟﺍ ةدﺎﻤﻟا 1

: تﺎﻴﺿﺎﻳﺮﻟا

ﻯﻭﺘﺴﻤﻟﺍ :

ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا

: ع . د

لﻭﻷﺍ ﻥﻴﺭﻤﺘﻟﺍ لﺤ ):

ﻥ 4 (

(1 ﻥﻴﺩﺩﻌﻠﻟ ﺭﺒﻜﻷﺍ ﻙﺭﺘﺸﻤﻟﺍ ﻡﺴﺎﻘﻠﻟ ﺔﻨﻜﻤﻤﻟﺍ ﻡﻴﻘﻟﺍ ﻥﻴﻴﻌﺘ ﺏ َﻭ ا

:

...

)...

ﻥ1.25 (

ﺎﻨﻴﺩﻟ = ∂

ﻥ 3 + ﺏ َﻭ 2 =

ﻥ 7 – ﻊﻤ 5

∋ ن .*ℵ

ﻥﻴﺩﺩﻌﻠﻟ ﻙﺭﺘﺸﻤ ﻡﺴﺎﻗ ﻕ ﺽﺭﻔﻨ ﺏ ﻭ ∂

.

ﻕ ﻥﺫﺇ

∂ | ﻕ َﻭ ﻕ ﻪﻨﻤﻭ ﺏ |

|

∂ 7 - ﺏ 3 .

ﺙﻴﺤﻭ

∂ 7 - ﺏ 3 = .29

ﻲﻫ ﺭﺒﻜﻷﺍ ﻙﺭﺘﺸﻤﻟﺍ ﻡﺴﺎﻘﻠﻟ ﺔﻨﻜﻤﻤﻟﺍ ﻡﻴﻘﻟﺍ ﻥﺫﺇ ﻲﻟﻭﺃ ﺩﺩﻋ 29 ﻭﺃ 1

.29

(2 ﺩﻋﻷﺍ ﻥﻴﻴﻌﺘ ﺔﻴﻌﻴﺒﻁﻟﺍ ﺩﺍ

ﺎﻬﻠﺠﺃ ﻥﻤ ﻥﻭﻜﻴ ﻲﺘﻟﺍ ن ﻭﻫ ﺭﺒﻜﻷﺍ ﻙﺭﺘﺸﻤﻟﺍ ﻡﺴﺎﻘﻟﺍ

: 29

)...

ﻥ1.25 (

ﻊﻀﻨ

[ ]

:

[ ]

_^



≡

≡ ﺏ 0 29

0

29 ا

ﻥﺫﺇ

[ ]

[ ]

_^



−

≡ +

≡

7 5 0 29

3 2 0 29

ن ن

[ ]

ﻥﺫﺇ

[ ]

_^



≡

≡

− 7 5 29

3 2 29

ن ﻥﺫﺇ ن

( ) [ ]

( ) [ ]

_^



≡

≡

−

28 0 2 29 ﺏﺭﻀﻟﺎﺒ

ﻲﻓ 4

30 20 29 ﺏﺭﻀﻟﺎﺒ

ﻲﻓ 10

ن ن

[ ]

ﻪﻨﻤ

[ ]

_^



≡ +

≡

− - 20 29

20 29

ن ﻥﺫﺇ ن

[ ]

:

[ ]

_^



≡

≡ ن ن 9 29

9 29

ﻪﻨﻤﻭ ﻡﻴﻗ ﻲﻫ ﺔﺒﻭﻠﻁﻤﻟﺍ ن = ن

+ 9 ﻙ 29 / ﻙ ﻊﻤ

∋ .ℵ

(3 ﺔﻴﻌﻴﺒﻁﻟﺍ ﺩﺍﺩﻋﻷﺍ ﻥﻴﻴﻌﺘ ﻥﻭﻜﻴ ﻰﺘﺤ α

αا

≡ ] 1 [3

)...

ﻥ1.5 (

ﺎﻨﻴﺩﻟ : = ∂ ﻥ 3 + ﻪﻨﻤﻭ 2

∂

≡ ] 2 [3

[ ]

3 ²2 ≡ ²ا ﻱﺃ

[ ]

3 1≡ ²ا :

[ ]

_{3 2} ≡ ^3ا ﻭ

ﻪﻨﻤﻭ :

∀

∋ﻩ : ℵ

[ ]

31≡ ^ـﻫ2ا

[ ]

32 ≡ ^1+ـﻫ2ا

ﻡﻴﻗ ﻥﺫﺇ ﻲﻫ ﺔﺒﻭﻠﻁﻤﻟﺍ α

= α 2 / ﻩ

∋ﻩ .ℵ

ﻲﻨﺎﺜﻟﺍ ﻥﻴﺭﻤﺘﻟﺍ ):

ﻥ 4 (

ﺎﻨﻴﺩﻟ : ﺎﺘ ) ﺹ

(

_{ﺕ8 7}

)

_ﺹ

(

_{ﺕ 4}

)

_ﺹ= ( ﺹ

4 7

ﺕ + + − +² − −³

) ...

(I

(1 ﺎﺘ ﻥﺃ ﺕﺎﺒﺜﺇ )

ﺹ ( ﺎﻓﺭﺼ ﺎﻴﻠﻴﺨﺘ ﺍﺭﺫﺠ لﺒﻘﻴ

1ﺹ :

)...

ﻥ1 (

ﻊﻀﻨ ﺹ :

ﺕ₁α =₁ /

1α

∋

( )

ﺕ

⁽

ﺕ8 7

⁾ ( )

ﺕ

⁽

ﺕ؛ 4

⁾ ( ) ( )

ﺕ ﺕ ﺎﺘ 4

7

ﺕ + + ₁α − +² ₁α − −³ ₁α = ₁α

=

− +

− +

+ +

+4 α8 ﺕ α7 ﺕ α α4 ﺕ α 7

ﺕ _{1 1} ²₁ ²₁ ³₁

(

7⁺₁α7^{+ 2}₁α⁻³₁α-

)

ﺕ⁺4⁺₁α8⁺²₁α4⁼

( )

( )

^{α α 0}

⁽

^{ت α}

⁾

^ﺎﺗ

4 α 8 α 4

3 1 1 2 1 1

21 1

7 α 7 0 ...

2

0 . . ..

.

1 ⇔ =



 + 

+

=

− + +

= _-

ﺔﻟﺩﺎﻌﻤﻟﺍ لﺤﺒ )

(1 ﻥﻴﻠﺤﻟﺍ ﺩﺠﻨ

َα

ًα 1−=₁ =₁ ﻑﻋﺎﻀﻤ لﺤ ﻱﺃ

ﻭ ) - (1 ﺔﻟﺩﺎﻌﻤﻠﻟ لﺤ ﺎﻀﻴﺃ ﻭﻫ )

) (2 ﺽﻴﻭﻌﺘﻟﺎﺒ ﻙﻟﺫ ﻥﻤ ﻕﻘﺤﺘﺘ .(

ﻥﺃ ﺞﺘﻨﺘﺴﻨ ﺍﺫﻫ ﺩﻌﺒ

1ﺹ = - ﺏﻭﻠﻁﻤﻟﺍ ﻑﺭﺼﻟﺍ ﻲﻠﻴﺨﺘﻟﺍ لﺤﻟﺍ ﻭﻫ ﺕ

(2 ﺔﺒﻜﺭﻤﻟﺍ ﺩﺍﺩﻋﻷﺍ ﻥﻴﻴﻌﺘ ، α

، β ﺎﺘ ﺙﻴﺤﺒ γ )

ﺹ

(

^γ+_ﺹ^β+2_ﺹ^α

)

⁽_ﺕ⁺_ﺹ⁾ = ( :

)...

ﻥ1 (

ﺎﻨﻴﺩﻟ : ﺎﺘ ) ﺹ

(

^γ+_ﺹ^β+2_ﺹ^α

)

⁽_ﺕ⁺_ﺹ⁾ = (

( )II .... ﺕγ+ﺹ

(

γ+ﺕβ

)

+²ﺹ

(

β+ﺕα

)

+³ﺹ α =

ﻥﻴﺒ ﺔﻘﺒﺎﻁﻤﻟﺎﺒ ﻥﻴﺘﻐﻴﺼﻟﺍ

) (I ﻭ ) (II ﺩﺠﻨ :















= +

+

=

−

+

=

− +

=

ﺕ γ 4 7 ﺕ

ﺕβ 7 γ

8 ﺕ

ﺕ α 4 β

ﺕ

1 α ﻪﻨﻤﻭ

:











=

−

=

−

=

β α α

4

7 4 ﺕ

1

* ﺎﺘ ﺔﻟﺩﺎﻌﻤﻟﺍ لﺤ )

ﺹ = ( 0

ﺎﺘ ﺎﻨﻴﺩﻟ ) ﺹ

(

_ﺕ4-7⁺_ﺹ4⁻²_ﺹ

)

⁽_ﺕ⁺_ﺹ⁾ = (

ﺎﺘ ) ﺹ

= (

⇔ 0

(

ﺕ4-7 ﺹ4 ﺹ

)

⁽ﺕ ﺹ⁾

0= + −² +

) ⇔

ﺹ + ﺕ = 0 ﺹ∨ 4 ﺹ 7 - 4

ﺕ + −²

= ( 0

) ⇔ ﺹ = - ﺕ ﺹ ∨

4 ﺹ 7 - 4

ﺕ + −²

= )... 0 ( (3

ﺔﻟﺩﺎﻌﻤﻟﺍ لﺤﻨ )

(3 ﺭﺼﺘﺨﻤﻟﺍ ﺯﻴﻤﻤﻟﺍ لﺎﻤﻌﺘﺴﺎﺒ

∆َ.

ﺎﻨﻴﺩﻟ

(

ﺕ4 7

) ( ) ( )

1 2 َ∆ : 3

4

ﺕ + −= − −² − =

)...

ﻥ0.25 (

ﺩﺩﻌﻠﻟ ﻥﺎﻴﻌﻴﺒﺭﺘﻟﺍ ﻥﺍﺭﺫﺠﻟﺍ ﺏﺴﺤﻨ َ∆

= - + 3 ﺕ4

ﻊﻀﻨ ﻙﻟﺫﻟ :

= δ ﺱ + ﻭ ﻉ ﺕ δ

َ∆= ² ) / ﻉ ، ﺱ (

∋

2؛

ﻥﺫﺇ

2δ

2

2ﻉ ﺱ

2 ﺕ ﺱ

ﻉ + − =

( ) ( )

δ

∆ δ

∆

2 2

2 2 2

َ 2 ﺱ ﻉ 4

ﺱ ﻉ 3

َ ﺱ

ﻉ 2

ﺱ ﻉ 3

ﺱ ﻉ 3

4

2 2 2 2

2

=

⇔











=

−

−=

=

⇔











= +

=

−

+

=

−

+ ^ق

ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ لﺤﻟﺍ ةدﺎﻤﻟا 1

: تﺎﻴﺿﺎﻳﺮﻟا

ﻯﻭﺘﺴﻤﻟﺍ :

ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا

: ع . د

( ) ( )

( )

^_







=

−

=

−

+

=

ﺱ ﻉ 2 ...

ﹷﺠ

ﺱ ﻉ 3

....

َﺏ

ﺱ ﻉ 5 ....

َ

2 2

2

ا 2

ﺠﺒ ﻊﻤ ) ( ∠ َﻭ )

َﺏ ( ﺩﺠﻨ ﻑﺭﻁﻟ ﺎﻓﺭﻁ :

2 ﺱ 2=² ﻪﻨﻤﻭ ﺱ 1=²

ﻱﺃ : ﺱ = 1 ﺱ ∨ = - 1

ﺱ ﺎﻤﻟ = ﺏﺴﺤ ﺩﺠﻨ 1 )

ﹷﺠ ( ﻉ = 2

ﺱ ﺎﻤﻟ = - ﺏﺴﺤ ﺩﺠﻨ 1 )

ﹷﺠ ( ﻉ = - 2

ﻪﻨﻤﻭ : = δ + 1 ﻭﺃ ﺕ 2 = δ

- – 1 ﺕ 2

...

)...

ﻥ0.5

(

ﺔﻟﺩﺎﻌﻤﻟﺍ ﻲﻠﺤ ﻥﻵﺍ ﺏﺴﺤﻨ )

.(3

2ﺹ

،

3ﺹ

ﺹ 2

1 2

ﺕ + + = ₂ َﻭ

ﺹ 2

1 2

ﺕ − − = ₃

ﻱﺃ ﺹ 3

2

ﺕ + = ₂ َﻭ

ﺹ 1

2

ﺕ − = ₃

...

)...

ﻥ0.5 (

ﺔﺼﻼﺨﻟﺍ :

ﺎﺘ ﺔﻟﺩﺎﻌﻤﻟﺍ لﻭﻠﺤ )

ﺹ = ( ﻲﻫ 0

1ﺹ = - ، ﺕ ﺹ

3 2

ﺕ + = ₂ ﻭ

ﺹ 1

2

ﺕ − = ₃

(3 ﺓﺭﻭﺼ ∂

1ﺹ ﺓﺭﻭﺼ ﺏ ،

2ﺹ ﺓﺭﻭﺼ ـﺠ ،

3ﺹ .

ﻥﺫﺇ ) ∂ ، 0 - (1 ﺏ ، ) ، 3 (2 ـﺠ ، ) ، 1 - .(2

ﺙﻠﺜﻤﻟﺍ ﻥﺃ ﺕﺎﺒﺜﻹ ﻲﻓ ﻡﺌﺎﻗ ـﺠ ﺏ ∂

ﻪﻋﻼﻀﺃ لﺍﻭﻁﺃ ﺏﺴﺤﻨ ∂

ﻪﻴﻓ ﺔﻘﻘﺤﻤ ﺕﻨﺎﻜ ﺍﺫﺇ ﺕﺭﻭﻏﺎﺜﻴﻓ ﺔﻴﺭﻅﻨ ﺭﺒﺘﺨﻨﻭ .

ﺎﻨﻴﺩﻟ (1 2) (0 3) ﺏا :

18=² + +² − =²

(

1 2

) (

0 1

)

ـﺠا 2=² + − +² − =²

(

_{2 2}

) (

_{3 1}

)

_{ـﺠ ﺏ} 20=² − − +² − =²

ﻥﺃ ﻅﺤﻼﻨ ا

ا ﺏ

ـﺠ ﺏ

ـﺠ ^{2 2}

2 = +

ﻪﻨﻤﻭ ﻓ ﻡﺌﺎﻗ ﺙﻠﺜﻤ ـﺠ ﺏ ∂

ﻲ ∂

)...

ﻥ0.5 (

ﺏ – ﺙﻠﺜﻤﻟﺎﺒ ﺔﻁﻴﺤﻤﻟﺍ ﺓﺭﺌﺍﺩﻟﺍ ﺔﻟﺩﺎﻌﻤ ﺔﺒﺎﺘﻜ ـﺠ ﺏ ∂

.

ﺯﻤﺭﻟﺎﺒ ﺓﺭﺌﺍﺩﻟﺍ ﻩﺫﻬﻟ ﺯﻤﺭﻨ )ﺩ

.(

ﻥﺃ ﺎﻤﺒ ﺏ ∂

ج ﻲﻓ ﻡﺌﺎﻗ ﺙﻠﺜﻤ ﻊﻠﻀﻟﺍ ﻭﻫ ﻩﺭﺘﻭ ﻥﺈﻓ ∂

] ﺏ [ ج ﻑﺼﺘﻨﻤﻭ ]

ﺏ [ج ﻩﺫﻫ ﺯﻜﺭﻤ ﻭﻫ

ﻊﻤ ﺓﺭﺌﺍﺩﻟﺍ ]

ﺏ [ج ﺎﻬﻟ ﺭﻁﻗ .

ﺽﺭﻔﺒ ﻑﺼﺘﻨﻤ ω

] ﺏ [ج ﻟ ﺎﻨﻴﺩ : ) ω 2

ﺱ

، ﺱ 2

ﻉ

ﻉ _{ﺏ ـﺠ ﺏ}

ـﺠ + +

( ﻕﻨ َﻭ 2ﺏ =

ـﺠ

ﻥﺫﺇ ) ω ، 2 (0 ﻕﻨ ﻭ 202

5^ق = ^ق .

) ﺩ

( )

₅ ²

(

_{0 ﻉ}

)

²

(

_{2 ﺱ}

)

: (

2 ^ق = − + −

(

_{2 ﺱ}

)

ﻉ

5=² +² − ﺔﺒﻭﻠﻁﻤﻟﺍ ﺓﺭﺌﺍﺩﻟﺍ ﺔﻟﺩﺎﻌﻤ ﻲﻫﻭ

.

)...

ﻥ0.25 (

ﺔﻟﺄﺴﻤﻟﺍ لﺤ ):

ﻥ 12 (

ﺎﻨﻴﺩﻟ : ( )_{ﺱ ﺎﺘ} ﺱ

5 ﺱ

6 1

2 =

− +

(1 ﺎﺘ ﺔﻟﺍﺩﻟﺍ ﺕﺍﺭﻴﻐﺘ ﺔﺴﺍﺭﺩ :

...

)...

ﻥ3 (

ﻰﻠﻋ ﻕﺎﻘﺘﺸﻺﻟ ﺔﻠﺒﺎﻗﻭ ﺓﺭﻤﺘﺴﻤﻭ ﺔﻓﺭﻌﻤ ﺎﺘ ﺔﻟﺍﺩﻟﺍ - ℜ

} ، 2 {3

ﻥﻷ ﺱ 5 ﺱ 6

0= + −² ) ⇔

ﺱ = 2 ﺱ ∨ = (3

ﺱ -

∞ 2

+ 3 ∞

ﺱ 5 ﺱ 6+ −² +

- +

( )ﺱ ﺎﺘ ﺎﻬﻨﺱ

0= ∞+←

ﻥﻷ

(

6+ﺱ5−²ﺱ

)

←

∞+

←

( )

←ﺱ 2 ﺱ

2 ﺎﻬﻨ ﺱ ﺎﺘ ﺎﻬﻨ ﺱ

5 ﺱ

6 1

2 _〉 = _〉

−

= +

∞+

ﻥﻷ

←

(

_{6 ﺱ5 ﺱ}

)

0 ^〈 + −²

← ( )

←ﺱ 2 ﺱ

2ﺎﻬﻨ ﺱ ﺎﺘ ﺎﻬﻨ ﺱ

5 ﺱ

6 1

2 _〈 = _〈

−

= +

∞−

ﻥﻷ

←

(

_{6 ﺱ5 ﺱ}

)

0 ^〉 + −²

←

( )

←ﺱ 3 ﺱ

3ﺎﻬﻨ ﺱ ﺎﺘ ﺎﻬﻨ ﺱ

5 ﺱ

6 1

2 _〉 = _〉

−

= +

∞−

ﻥﻷ

←

(

_{6 ﺱ5 ﺱ}

)

0 ^〉 + −²

←

( )

←ﺱ 3 ﺱ

3ﺎﻬﻨ ﺱ ﺎﺘ ﺎﻬﻨ ﺱ

5 ﺱ

6 1

2 _〈 = _〈

−

= + ﻥﻷ ∞+

←

(

_{6 ﺱ5 ﺱ}

)

0 ^〈 + −²

- ﺎﻬﺘﺭﺎﺸﺇ ﺔﺴﺍﺭﺩﻭ ﺔﻘﺘﺸﻤﻟﺍ ﺔﻟﺍﺩﻟﺍ ﺏﺎﺴﺤ .

(

₆⁵_ﺱ^ﺱ₅^{2 2}_ﺱ

)

^{( )ﺱ ﹶﺎﺘ}

2 =

− +

− +

ﹶﺎﺘ ) ﺱ = (

⇔ 0 ﺱ 25 =

ﹶﺎﺘ ) ﺱ (

<

⇔ 0 ﺱ 2 >

ﹶﺎﺘ َﻭ 5 )

ﺱ (

>

⇔ 0 ﺱ 2 <

5

ﺇ ﻥﻴﻟﺎﺠﻤﻟﺍ ﻥﻤ لﻜ ﻰﻠﻋ ﹰﺎﻤﺎﻤﺘ ﺓﺩﻴﺍﺯﺘﻤ ﺎﺘ ﻥﺫ [

- ، ∞ ] 2 ﻭ [ ، 2 25 ]

ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ لﺤﻟﺍ ةدﺎﻤﻟا 1

: تﺎﻴﺿﺎﻳﺮﻟا

ﻯﻭﺘﺴﻤﻟﺍ :

ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا

: ع . د

ﺔﺼﻗﺎﻨﺘﻤ ﺎﺘ ﻥﻴﻟﺎﺠﻤﻟﺍ ﻥﻤ لﻜ ﻰﻠﻋ ﹰﺎﻤﺎﻤﺘ

25 [ ، ] 3 ﻭ [ ، 3 + ] ∞

ﺕﺍﺭﻴﻐﺘ لﻭﺩﺠ :

- ﺱ ∞ 2

25 + 3

∞

ﹶﺎﺘ ) ﺱ ( + + -

-

ﺎﺘ ) ﺱ ( + ∞

- + 4

∞

0 -

∞ -

∞ 0

* (2 ﻉ ﻭ ﺱ ﺔﻟﻻﺩﺒ َﻉ ﻭ َﺱ ﻥﻋ ﺭﻴﺒﻌﺘﻟﺍ :

ﺕ : ) ن ﻉ ، ﺱ (

↵ َن )

َﻉ ، َﺱ (

ﺙﻴﺤ ﺓﺭﻴﻅﻨ َن

ﻡﻴﻘﺘﺴﻤﻠﻟ ﺔﺒﺴﻨﻟﺎﺒ ن )

ﻕ : ( ﺱ 2 = 5

ﻥﺫﺇ

 :







=

= +

َﻉ ﻉ َﺱ 2ﺱ 25

ﻪﻨﻤﻭ

 :





=

=

−

َﻉ ﻉ

َﺱ 5 ﻭ ﺱ . ـﻫ . ﻡ

)...

ﻥ0.5 (

ﺓﺭﻭﺼ ﻥﻋ ﺙﺤﺒﻟﺍ • )

ﻯ ( ﺕ ﺭﻅﺎﻨﺘﻟﺎﺒ :

ﺔﻟﺩﺎﻌﻤ ﻲﻓ ﺽﻭﻌﻨ ﻡﺜ َﻉ َﻭ َﺱ ﺔﻟﻻﺩﺒ ﻉ َﻭ ﺱ ﺏﺘﻜﻨ • )

ﻯ .(

نذإ

 :





=

=

− ﻉ

َﻉ

ﺱ 5

َﺱ

ﺎﻨﻴﺩﻟ : ﺱ ﻉ 5 ﺱ

6 1

2 =

− ﺘﻟﺎﺒ ﻥﺫﺇ +

ﺩﺠﻨ ﺽﻴﻭﻌ :

(

َﺱ 5

) (

5 َﺱ 5

)

^َﻉ

6

1 2 =

−

−

− ﻪﻨﻤﻭ +

:

َﺱ َﻉ 5

َﺱ 6

1

2 =

− +

ﺔﻟﺩﺎﻌﻤ ﻲﻫﻭ )

َﻯ ( ﺓﺭﻭﺼ ) ﻯ ( ﺕ ﺭﻅﺎﻨﺘﻟﺎﺒ

)...

ﻥ0.25 (

ﺔﻟﺩﺎﻌﻤ ﻥﺃ ﻅﺤﻼﻨ )

َﻯ ( ﺔﻟﺩﺎﻌﻤ ﺎﻬﺴﻔﻨ ﻲﻫ )

ﻯ (

ﻥﺫﺇ )

َﻯ ( ﻰﻠﻋ ﻕﺒﻁﻨﻤ )

ﻯ ( ﻲﻠﻴ ﺎﻤ ﺞﺘﻨﺘﺴﻨ ﻪﻨﻤﻭ :

ﻡﻴﻘﺘﺴﻤﻟﺍ )

ﻕ : ( ﺱ 2 = ﻰﻨﺤﻨﻤﻟﺍ ﺭﻅﺎﻨﺘ ﺭﻭﺤﻤ ﻭﻫ 5 )

ﻯ (

)...

ﻥ0.25 (

(3 ﺱﺎﻤﻤﻟﺍ ﺔﻟﺩﺎﻌﻤ ﺔﺒﺎﺘﻜ )

(∆ ﻰﻨﺤﻨﻤﻠﻟ )

ﻯ ( ﺔﻠﺼﺎﻔﻟﺍ ﺕﺍﺫ ﺔﻁﻘﻨﻟﺍ ﻲﻓ ﺱ

4=₀ :

) : (∆ ﻉ = ﹶﺎﺘ ) ) (4 ﺱ – + ( 4 ﺎﺘ ) .(4

ﺎﻨﻴﺩﻟ

( )

_{4 ﺎﺘ} : 16

20

6 1

21 =

−

= + ﹶﺎﺘ َﻭ )

= (4

( ) ( )

⁴₂²

4 5 3

2

−

= + . −

ﻥﺫﺇ ) : (∆ ﻉ = 4 - )3 ﺱ – + (4 21 ) : (∆

ﻉ = 4 - ﺱ3 2+ 7

)...

ﻥ0.75 (

ﻰﻨﺤﻨﻤﻠﻟ ﺔﻴﺌﺎﻬﻨﻼﻟﺍ ﻉﻭﺭﻔﻟﺍ ﺔﺴﺍﺭﺩ )

ﻯ : (

)...

ﻥ1 (

ﺎﻴﺎﻬﻨﻟﺍ ﺔﺴﺍﺭﺩ ﺏﺴﺤ ﻥﺃ ﺞﺘﻨﺘﺴﻨ ﺕ

) ﻯ ( لﺒﻘﻴ ﺔﺒﺭﺎﻘﻤ ﺕﺎﻤﻴﻘﺘﺴﻤ ﺙﻼﺜﻭ ﺔﺒﺭﺎﻘﻤ ﺔﻴﺌﺎﻬﻨ ﻻ ﻉﻭﺭﻓ 6

ﻉ ﺎﻬﺘﻻﺩﺎﻌﻤ =

ﺱ ، 0 = ﺱ ، 2 =

.3

) ﻯ ( ﻊﻁﻘﻴ ) ﻉ َﻉ ( ﻙ ﺔﻁﻘﻨﻟﺍ ﻲﻓ )

، 0 61 (

ﻡﺴﺭ ﺭﻅﻨﺃ )

ﻯ ( ﺔﺤﻔﺼﻟﺍ ﻲﻓ /8

.8

...

)....

ﻥ1.5 (

(4 لﺎﺠﻤﻟﺍ ﻰﻠﻋ ﺎﺘ ﺭﺎﺼﺘﻗﺍ ﻭﻫ ﺎﻫ [

، 3 + ] ∞

)...

ﻥ0.5 (

ﺎﻤﺎﻤﺘ ﺔﺼﻗﺎﻨﺘﻤﻭ ﺓﺭﻤﺘﺴﻤ ﺎﺘ ﺔﻟﺍﺩﻟﺍ ﻥﺃ ﻅﺤﻼﻨ )

ﺎﻤﺎﻤﺘ ﺔﺒﻴﺘﺭ (

لﺎﺠﻤﻟﺍ ﻰﻠﻋ [

، 3 + ] ∞ ﺍﺫﻬﻟ لﺒﺎﻘﺘ ﻥﺫﺇ ﻲﻬﻓ

لﺎﺠﻤﻟﺍ ﻲﻓ لﺎﺠﻤﻟﺍ [

، 0 + .]∞

ﺎﺘ ﺭﺎﺼﺘﻗﺍ ﻥﺫﺇ

"

ﺎﻫ

"

ﻥﻤ ﻲﻠﺒﺎﻘﺘ ﻕﻴﺒﻁﺘ ﻭﻫ [

، 3 + ]∞ ﻭﺤﻨ [ ، 0 + ]∞ ﺔﻴﺴﻜﻋ ﺔﻟﺍﺩ لﺒﻘﺘ ﺎﻫ ﻲﻟﺎﺘﻟﺎﺒﻭ ﺎﻫ

1−

ﺎﻫ

1−

لﺎﺠﻤﻟﺍ ﻰﻠﻋ ﺎﻤﺎﻤﺘ ﺔﺼﻗﺎﻨﺘﻤﻭ ﺓﺭﻤﺘﺴﻤﻭ ﺔﻓﺭﻌﻤ [

، 0 + ] ∞ لﺎﺠﻤﻟﺍ ﻲﻓ ﺎﻬﻤﻴﻗ ﺫﺨﺄﺘﻭ [

، 3 + ]∞

ﺔﻟﺍﺩﻟﺍ ﺕﺍﺭﻴﻐﺘ لﻭﺩﺠ ﺎﻫ

1−

ﻤ ﻡﺴﺭ ﻲﻓ ﺎﻨﺩﻋﺎﺴﻴ ﺎﻫﺎﻨﺤﻨ

ﻯ )

-

.(1

)...

ﻥ0.75 (

ﺱ + 0

∞

ﺎﻫ

1−

)َ

ﺱ ( -

ﺎﻫ

1−

) ﺱ ( +

∞

3

ﻥﺃ ﻡﻭﻠﻌﻤﻟﺍ ﻥﻤ )

ﻯ ( ﻭ ) ﻯ

-

(1

ﺎﻨﺘﻤ ﻉ ﻪﺘﻟﺩﺎﻌﻤ ﻱﺫﻟﺍ لﻭﻷﺍ ﻑﺼﻨﻤﻠﻟ ﺔﺒﺴﻨﻟﺎﺒ ﻥﺍﺭﻅ =

ﺱ .

ﻰﻨﺤﻨﻤﻠﻟ ﺱﺎﻤﻤﻟﺍ ﺔﻟﺩﺎﻌﻤ )

ﻯ

-

(1

ﺔﻠﺼﺎﻔﻟﺍ ﺕﺍﺫ ﺔﻁﻘﻨﻟﺍ ﺩﻨﻋ 21

.

) )َ∆ : ﻉ

=

2 ﺎه س 1 2 ﺎه 1 2

1 1− ^َ1−



 







 

 −

 +



 





( ) ( ) _ﺎﻫ

21 ﺱ ﺎﻫ 21 ﺱ

ﺎﺘ 2 ﺱ

1 1−



 



=

⇔

=

⇔

=

ﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴ

لﺤﻟﺍ ةدﺎﻤﻟا 1

: تﺎﻴﺿﺎﻳﺮﻟا

ﻯﻭﺘﺴﻤﻟﺍ :

ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا

: ع . د

ﺎﺘ ) ﺱ 2 = (

⇔ 1 ﺱ = ﻕﺒﺴ ﺎﻤ ﺏﺴﺤ 4 .

( ) ( ) 2 ^ﺎه

1

َﺎه 4

1

َﺎﺗ 4

1 1

3

4 ^َ1

43

 −



 



=

=

− =

=

) −

ﻕﺒﺴ ﺎﻤ ﺏﺴﺤ (

ﻪﻨﻤﻭ ) : )َ∆ : ﻉ

=

 −



 

 − + ﺱ 34

21 4

) )َ∆ : ﻉ

=

− +ﺱ34 143 .

(5 ﻥﻴﻴﻌﺘ ﻥﻴﺩﺩﻌﻟﺍ ﺙﻴﺤ ﺏ ﻭ ∂

:

)...

ﻥ1 (

ﺱ ∀

∋ -ℜ } ، 2 {3 ﺎﺘ ) ﺱ ﺱ = ( 3 ﺱ 2ﺏ

+ −

−

ا

ﺎﻨﻴﺩﻟ : ﺎﺘ ) ﺱ ﺱ = ( 3 ﺱ 2ﺏ

+ −

− = ا

( ) ( )

(

₂^ﺏ_ﺱ³

) (

₃^{ﺱ ﺏ}_ﺱ

)

2 − −

+

−

+ ا

. ا

ﺩﺠﻨ ﺔﻘﺒﺎﻁﻤﻟﺎﺒ

 :



 +

=

−

+

= 3 2 ﺏ 1

ﺏ 0

ا

ﻪﻨﻤﻭ

 :





= +

= ﺏ 1

- 1 ا

ﻥﺫﺇ : ﺱ ∀

∋ -ℜ } ، 2 {3 ﺎﺘ ) ﺱ ﺱ = ( 31- ﺱ

2 1 + −

−

* ﻡ ﺏﺎﺴﺤ ﺔﻟﻻﺩﺒ ن

: ن

)...

ﻥ1 (

ﻡ ﺎﻨﻴﺩﻟ = ن

ﺎﺘ ) + (4 ﺎﺘ ) + (5 ﺎﺘ ) + . . . + (6 ﺎﺘ

) (ن ﺙﻴﺤ

∋ ن ﻥ ﻭ ℵ

<

3

ﻡ ﺩﻭﺩﺤ ﺏﺴﺤﻨ ﻲﻠﻴ ﺎﻤﻜ ن

:

( )

_{4 ﺎﺘ}

11 21 + − =

( )

_{5 ﺎﺘ}

12 3

1 + − =

( )

_{6 ﺎﺘ}

13 4

1 − =

+

( )_{7 ﺎﺘ} 14

5

1 + − =

( )ﺎﺘ 31

21 ن

ن

ن =

− + −

−

ﺩﺠﻨ ﻑﺭﻁﻟ ﺎﻓﺭﻁ ﻊﻤﺠﻟﺎﺒ :

ﺎﺘ ) + (4 ﺎﺘ ) + (5 ﺎﺘ ) + ... + (6 ﺎﺘ

) = (ن - + 1

−ن 21

ﻥﺫﺇ : ﻡ 2 1 1

ن + −= ن

−

ﺏﺎﺴﺤ

ن ﻡ∞+ﺎﻬﻨ←ن

:

...

)...

ﻥ0.5 (

ن ﻡ∞+ﺎﻬﻨ←ن ن =

ن ∞+←

 +

= −

− 1- ﺎﻬﻨ

21 ) 1

ن ﻥﻷ

← − 21 (0