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

If x = 1 + a + `a^(2) + …. infty " , " y = 1 + b + b^(2) + …. infty, " " |a| lt 1 , |b| lt 1, ` then ` 1 + ab + a^(2) b^(2) + ….. infty = `

A

`(xy)/(x+y)`

B

`(x+y+1)/(xy)`

C

`(xy)/(x-y)`

D

`(xy)/(x+y-1)`

Text Solution

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The correct Answer is:
D
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ARIHANT SSC-SEQUENCE, SERIES & PROGRESSIONS-INTRODUCTORY EXERCISE 18.2
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  2. Find the sum of n terms of the series 1+3 +7 +15 + …

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

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  4. Find the sum to n terms of the series 11+ 102+1003+10004+… :

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  5. Find the sum of first n groups of (1) + (1+3) +(1+3+9) + (1+3+9 +27) +...

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  6. Find the sum to n terms of the following series : 2+5+14+41 + …

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

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

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

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

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

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

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

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  14. In a set of four number, the first three are in GP & the last three ar...

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

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

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

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

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

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

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