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The sum of series 1 + 2x + 3x^(2) + 4x^(...

The sum of series `1 + 2x + 3x^(2) + 4x^(3) + ......` up to infinity when `x` lies between `0` and `1` i.e., `0 lt x lt 1` is

A

`(1-x)^(-2)`

B

`(1+x)^(-2)`

C

`(1-x)^(2)`

D

`(1+x)^(2)`

Text Solution

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The correct Answer is:
b
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PREMIERS PUBLISHERS-BINOMIAL THEOREMN,SEQUENCES AND SERIES -PROBLEMS FOR PRACTICE(Choose the correct option for the following)
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  2. Find the odd man out: For any two positive integers:

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  3. AM, GM, HM denote the arithmetic, geometric and harmonic means of a an...

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  4. Find the odd man out in the following:

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  5. Find the correct statement:

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  6. Find the correct statement:

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  7. Find the incorrect statement:

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  8. Assertion (A): In the expansion of (a +b)^(n) n in N the coefficient a...

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  9. Assertion: If a and b are distinct integers then (a - b) is a factor ...

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  10. With usual notation C(0) + C(2) + C(4) + ... is:

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  11. In the expansion of (2x + 3)^(5) the coefficient of x^(2) is:

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  12. In the expansion of (I + x)^(22) which term is the middle term:

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  13. AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic mea...

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  14. The sum of the first n terms of the series 1/(sqrt(2) + sqrt(5)) + 1/(...

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  15. The sum of series 1 + 2x + 3x^(2) + 4x^(3) + ...... up to infinity whe...

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  16. 1/(1!) + 1/(3!) + 1/(5!) + … is.

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  17. sqrt((1-2x)/(1+2x)) is approximately equal to:

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  18. Expansion of log(sqrt((1+x)/(1-x))) is :

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  19. The value of 1- 1/2(3/4) + 1/3(3/4)^(2) -1/4(3/4)^(3) + ... is:

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  20. Coefficient of x^(2) in (x^(2) + 1/x)^(6) is 1 (ii)1,4, 7 are in H.P...

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