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If |x| lt 1 then 1+n ((2x)/(1+x))+(n(n+1...

If `|x| lt 1` then `1+n ((2x)/(1+x))+(n(n+1))/(2!) ((2x)/(1=x))^2 + ….....oo=`

A

`((2x)/(1+x))^n`

B

`((1+x)^n)/(2x))^n`

C

`((1-x)/(1+x))^n`

D

`((1-x)/(1+x))^n`

Text Solution

Verified by Experts

The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1C (BINOMIAL THEOREM WITH RATIONAL INDEX)
  1. 1-(1)/(4)+(1.3)/(4.8)-(1.3.5)/(4.8.12)+…..=

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  2. 1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

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  3. 1-(1)/(8)+(1.3)/(8.16)-(1.3.5)/(8.16.24)+…..=

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  4. 1-(3)/(4)+(3.5)/(4.8)-(3.5.7)/(4.8.12)+….=

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  5. 1-(3)/(16)+(1.4)/(1.2)((3)/(16))^2- (1.4.7)/(1.2.3)((3)/(16))^3 + …..=

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  6. If x=(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…., then x^2+2x-2=

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  7. If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.

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  8. (1.3)/(3.6)+(1.3.5)/(3.6.9)+(1.3.5.7)/(3.6.9.12)+…=

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  9. (1.4)/(5.10)-(1.4.7)/(5.10.15)+(1.4.7.10)/(5.10.15.20)+….=

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  10. (3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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  11. (5)/(6.12)+(5.8)/(6.12.18)+(5.8.11)/(6.12.18.24)+…....=

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  12. (5)/(3.6)+(5.7)/(3.6.9)+(5.7.9)/(3.6.9.12)-…....=

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  13. (1)/(4)-(5)/(4.8)+(5.7)/(4.8.12)-…....=

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  14. (3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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  15. If x=(5)/((2!).3)+(5.7)/((3!).3^(2))+(5.7.9)/((4!).3^(3))+…. then fi...

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  16. If x=1+(3)/(1!)xx(1)/(6)+(3xx7)/(2!)((1)/(6))^(2)+(3xx7xx11)/(3!)((1)/...

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  17. 1+(n)/(2)+(n(n-1))/(2.4)+(n(n-1) (n-2))/(2.4.6)+…....=

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  18. 1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+n))^2+…..

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  19. If |x| lt 1 then 1+n ((2x)/(1+x))+(n(n+1))/(2!) ((2x)/(1=x))^2 + ….......

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  20. If y=2x+3x^2 + 4x^3 +…, then x I terms of y is

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