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If u(1), u(2), u(3),… form a G.P. with c...

If `u_(1), u_(2), u_(3),…` form a G.P. with common ratio k, find the sum of `u_(1)u_(2) + u_(2)u_(3)+….+u_(n)u_(n+1)` in terms of `u_(1)` and k.

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The correct Answer is:
`u_(1)^(2)k(k^(2n)-1)/(k^(2)-1)`
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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)
  1. If the sum of first n terms of G.P. is S and the sum of its first 2n t...

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  2. If S(n) = 1 + (1)/(2) + (1)/(2^(2))+….+(1)/(2^(n-1)), find the least v...

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  3. If u(1), u(2), u(3),… form a G.P. with common ratio k, find the sum of...

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  4. Find the sum to n terms of the following series: (x+1/x)^2+(x^2+1/(x^2...

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  5. If the first term, common ratio and the sum of first n terms of a G.P....

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  6. When a certain golf-ball is dropped on a piece of pavement, it bounces...

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  7. If the A.M. of two numbers be twice their G.M., prove that two numbers...

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  8. If A and G be the A.M. and G.M. of two numbers , show that the numbers...

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  9. If a, b, c form an A.P. and b, c, a form a G.P., show that (1)/(c ), (...

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  10. If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y)...

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  11. The sum of three numbers in A.P. is 15. If 1, 4 and 19 are added to th...

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  12. The sum of three numbers in A.P. is 18. If 2, 2, 6 are added respectiv...

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  13. Three terms are in G.P. Their product is 216. If 4 be added to the fir...

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  14. Find the sum to n terms of each of the following series : 1 + 11 + 1...

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  15. Find the sum to n terms of each of the following series : 2 + 22 + ...

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  16. 0.8 + 0.88 + 0.888 + …

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  17. Find the sum to n terms of each of the following series : 0.6 + 0.6...

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  18. Find the sum to n terms of each of the following series : 1 + 4 + 1...

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  19. Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G...

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  20. If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (...

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