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If a(1), a(2), a(3),…, a(n) be in A.P. S...

If `a_(1), a_(2), a_(3),…, a_(n)` be in A.P. Show that,
`(1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +….+(1)/(a_(n-1)a_(n)) = (n-1)/(a_(1)a_(n))`

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
  1. If a, b, c are in A.P. then show that, a((1)/(b)+(1)/(c )), b((1)/(c )...

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  2. Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqr...

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  3. If a(1), a(2), a(3),…, a(n) be in A.P. Show that, (1)/(a(1)a(2)) + (...

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  4. If a(1), a(2), a(3),…, a(2k) are in A.P., prove that a(1)^(2) - a(2)^(...

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  5. If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b...

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  6. Find the sum to n terms of each of the following series : 2.4 + 6.8 ...

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  7. Find the sum to n terms of each of the following series : 1^(2) + 3^...

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  8. Find the sum to n terms of each of the following series : 1.3 .5 + 3...

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  9. Find the sum of the following series : 3.1^(2) + 4.2^(2) + 5.3^(2) +...

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  10. Find the sum of the following series : 1+3+6+10+15+… to n terms.

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  11. Find the sum of the following series : 1+5+12+22+35+…. to n terms.

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  12. The sum of first n terms of a series is n^(2) + an + b. Show that b = ...

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  13. If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n...

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  14. Find the sum to n terms of each of the following series : (1) + (1+2...

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  15. Find the sum to n terms of each of the following series : (1^(2)) + ...

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  16. Find the sum to n terms of each of the following series : (3^(3) - 2...

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  17. Find the sum to n terms of each of the following series : (1) + (2+3...

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  18. Find the sum to n terms of each of the following series : (1)/(1.4) ...

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  19. Find the sum to n terms of each of the following series : (1)/(2.5) ...

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  20. Find the sum to n terms of each of the following series : n.1 + (n-1...

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