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If |r| gt 1, x = a + a/r + a/r^(2) + ......

If `|r| gt 1, x = a + a/r + a/r^(2) + .......... infty`, `y = b - b/r + b/r^(2) - ......... infty` and `z = c + c/r^(2) + c/r^(4) + ...... infty`, then the value of `(xy)/z = `

A

1

B

`r`

C

`(ab)/c`

D

`c/(ab)`

Text Solution

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The correct Answer is:
C
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NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -EXERCISE
  1. The AM and GM of two positive numbers are 15 and 9 respectively. The n...

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  2. If G is the GM between a and b the 1/(G + a) + 1/(G + b) =

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  3. If |r| gt 1, x = a + a/r + a/r^(2) + .......... infty, y = b - b/r + b...

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  4. If the p^(th) term if an A.P. is q and the q^(th) term of an A.P is p ...

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  5. The sum of the series 1^(2) + 3^(2) + 5^(2) + ......+n'

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  6. The sum of 10 terms of the series sqrt(2) + sqrt(6) + sqrt(18) + .... ...

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  7. If three positive real numbers a, b, c are in A.P and abc = 4, then th...

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  8. Sum to infininty of the series 1 + 4/5 + 7/5^(2) + 10/5^(3) + ...... i...

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  9. The sum of the series 2, 5, 8, 11, …… is 60100, then n is

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  10. Let a(n) be the n^(th) term of a G.P of positive integers. Let sum(n =...

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  11. cos x = b for what b do the roots of the equation form an A.P?

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  12. Sum of all terms in in G.P is 5 times the sum of odd terms. The common...

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  13. Sum of n terms of the serise sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) +...

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

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

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

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

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

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

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