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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/(1 + x)`

B

`1/(1 - x)`

C

`1/(1 - 2x)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -EXERCISE
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  2. Sum of n terms of the serise sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) +...

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

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  4. If log(3)^(2),log(3)(2^(x) - 5) and log(2^(x) - 7/2)are in A.P then th...

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  5. If the sum of first n positive integers is 1/5 times the sum of their ...

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  6. The second term of an A.P is (x - y) and fifth term is (x + y), then t...

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  7. Three numbers are in G.P. if we double the middle term, we get an A.P....

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  8. Three non zero numbers a, b, c are in A.P. Increasing a by 1 or increa...

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  9. If x gt 0 then the sum of the series e^(-x) - e^(-2x) + e^(-3x) .........

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  10. The sum of the series 0.4 + 0.004 + 0.00004 + infty is

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  11. If (1.05)^(50) = 11.658 then sum (n = 1) ^(49) (1.05)^(n) equals

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  12. The product of n positive numbers is 1, then their sum is a positive i...

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  13. If x, y, z are in A.P then e^(-x),e^(-y)and e^(-z) are

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  14. If the sum of the first n terms of a series be 5n^(2) + 2n, then its s...

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  15. If the sum of the first n terms of a series be 5n^(2) + 2n, then its s...

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  16. If A.M and G.M of the roots of a quadratic equation in x are p and q r...

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  17. If the 10^(th)term of G.P is 9 and 4^(th)term is 4 then its 7^(th)term...

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  18. If x gt 1, y gt 1, z gt 1 are in G.P then 1/(1 + log x),1/(1 + log y),...

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  19. Suppose a, b, c are in a.P and a^(2), b^(2), c^(2) are in G.P. If a lt...

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  20. If the 7^(th) term of n A.P is 40. Then the sum of its first 13 terms ...

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