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Sum of n terms of the series 1+2 x+3 x...

Sum of n terms of the series
`1+2 x+3 x^(2)+4 x^(3)+..,(x ne 1)` is

A

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

B

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

C

3)`((1-x)^(n))/((1+x)^(2))-(n x^(n))/(1+x)`

D

4)`(1+x^(n))/((1-x)^(n))-(n x^(n))/(1-x)`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. The n^(th ) term of the series 1+5+12+22+35+.. ..

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  2. Sum to n terms of the series2+6+12+20+.. is,

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  3. Sum of n terms of the series 1+2 x+3 x^(2)+4 x^(3)+..,(x ne 1) is

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  4. Sum of 25 terms of the series 1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))+.. ....

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  5. Sum of 25 terms of the series 1+2 . 2+3 . 2^(2)+4 . 2^(3)+5 . 2^(4)+...

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  6. The n^(th ) term of the series 1+4+13+40+.. .is

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  7. 3+5+7+ …..to n^(th) term is

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  8. The n^(th ) term of the series4+13+28+49+.. . Is

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  9. The sum 1^(2)+1+2^(2)+2+3^(2)+3+..+n^(2)+n is

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  10. Find the sum to n terms of the series 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)...

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  11. sum(n=1)^(n) (1)/((4 n-1)(4 / t+3))=

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  12. If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

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  13. The sum of first 9 terms of the series : ( 1^(3))/( 1) + ( 1^(3) + 2...

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  14. (1)/(1 . 4)+(1)/(4 . 7)+(1)/(7 . 10)+.. .. .. ..=

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  15. 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.. .. to infty=

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  16. Sum to n terms of the series3+15+35+63+.. ..

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  17. (1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n terms =

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  18. Sum of 10 terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1+2...

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  19. If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) +...

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  20. Sum of 25 terms of the series 1 . 3+2 . 5+3 . 7+.., is

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