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For absx lt1 the value of 1+3x+6x^2+10x^...

For `absx lt1` the value of `1+3x+6x^2+10x^3+.....t o infty` is

A

`4/(1-x)^4`

B

`3/(1-x)^3`

C

`1/(1-x)^3`

D

none of these

Text Solution

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The correct Answer is:
C
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The sum to infinity of the series 1+2/3+6/3^2+10/3^3+14/3^4+....

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  2. The sum to n terms of the series 1+2(1+1/n)+3(1+1/n)^2+....... is give...

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  3. For absx lt1 the value of 1+3x+6x^2+10x^3+.....t o infty is

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  4. If pth, qth, and rth term of an AP are equal to corresponding terms of...

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  5. If a,b,c are positive real number, then the least value of (a+b+c)(1/a...

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  6. An infinite GP has first term x and sum 5, then x belongs to

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  7. 2^(1/4),2^(2/8),2^(3/16),2^(4/32)......infty is equal to

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  8. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

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  9. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all x,yin N such ...

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  10. Sum of n terms of the series 8+88+888+....equals

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  11. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  12. The sum of integer in between 1 to 100 which is divisible by 2 or 5 is

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  13. 1/2+3/4+7/8+15/16+..... t o n terms =

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  14. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

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  15. If x in{1,2,3......9} and fn(x) =x x x ...x (n digits ), then fn^2(3)+...

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  16. Four no. are in AP . If their sum is 20 and the sum of their squares i...

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  17. Sum of n terms of series 1.3+3.5+5.7+....is

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  18. If the sum of an infinitely decreasing GP is 3, and the sum of the squ...

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  19. 1+2.2+3.2^2+4.2^3+....100.2^99 equals

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  20. If A1,A2 be two AM's and G1,G2 be the two GM's between two number a an...

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