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If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))...

If `|x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+......` is equal to

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Required value of
`(1-(2x)/(1+x))^(-n) = ((1+x-2x)/(1+x))^(-n) = ((1-x)/(1+x))^(-n) = ((1+x)/(1-x))^(n)`
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  3. sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...

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  4. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...

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  6. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...

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  7. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

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  8. Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...

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  9. sum(k=1)^ook(1-1/n)^(k-1)= n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

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  10. The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...

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  11. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+.... is equal to

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  12. 1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) + "….." is equal to

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  13. If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is ...

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  14. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

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  15. If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...

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  16. If x is positive, the first negative term in the expansion of (1 + x)^...

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  17. If x is so small that x^(3) and higher power of x may neglected, then ...

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  18. If the expansion in power of x of the function (1)/(( 1 - ax)(1 - b...

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  19. If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)x^(2)+"….", the b sum(r=1)^(50...

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