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Find the sum to n terms : 1+ 2x + 3x^...

Find the sum to n terms :
`1+ 2x + 3x^2 + 4x^3 + … ,xne 1` :

A

`1+nx^n`

B

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

C

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

D

`{1-x^n/(1-x)^2-nx^n/(1-x)}`

Text Solution

Verified by Experts

The correct Answer is:
D
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QUANTUM CAT-SEQUENCE, SERIES & PROGRESSIONS-QUESTION BANK
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  2. Find the sum to n terms of the following series : 2+5+14+41 + …

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  3. Find the sum to n terms : 1+ 2x + 3x^2 + 4x^3 + … ,xne 1 :

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  4. Find the sum to infinity of the series 1+3x+5x^2+7x^3+oow h e n|x|<1.

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  5. Find the sum to first n terms : 1+2/3 + 3/(3^2) + 4/(3^3)+….

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  6. Find the sum to n terms of 3 * 2 + 5*2^2 + 7*2^3 + ….

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  7. Find the sum of the series 1+4/5+7/(5^2)+10/(5^3)+...

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  8. Find the sum of the series : 1*3^2 + 2* 5^2 + 3*7^2 + … to 20 terms...

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  9. Sum up to 16 terms of the series (1^(3))/(1) + (1^(3) + 2^(3))/(1 + 3)...

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  10. In a set of four numbers the first three are in G.P and the llast thre...

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  11. The sum of an infinite G.P. is 16 and the sum of the squares of its te...

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  12. If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …...

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  13. A person is entitled to receive an annual payment which for each ye...

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  14. What is the the sum of the infinite geometric series 1/4 - 3/(16) + 9...

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  15. The sum of first two terms of a G.P. is 5/3 and the sum to infinity of...

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  16. A ball is dropped from a height of 96 feet and it rebounds 2/3 of the ...

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  17. Find the 10th term of the H.P. 1, 1/3 , 1/5 , 1/7 , 1/9 , 1/(11) ,….

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  18. If the 4th and the 7th terms of an H.P. are 1/2 and 2/7 respectively ....

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  19. Find the sum of n terms of the series 1+4/5+7/(5^2)+10+5^3+dot

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  20. Find the sum to n terms of the series 1+4/5+7/5^2+10/5^3+……find the su...

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