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If `a_1, a_2`, ............, `a_n` are in A.P. and `a_i >0` for all i , prove that : `1/(sqrt a_1+sqrt a_2)+1/(sqrt a_2+sqrt a_3)+.............+ 1/(sqrt (a_(n-1))+sqrt a_n)= (n-1)/(sqrt a_1+sqrt a_n)` .

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. For the A.P., a1, a2,a3, ............., if a4/a7= 2/3, find a6/a8.

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  2. If a1, a2,a3,..........., an be an A.P. of non-zero terms, prove that ...

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  3. If a1, a2, ............, an are in A.P. and ai >0 for all i , prove th...

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  4. If a1, a2,a3,..........., an are in A.P. with common difference d, pro...

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  5. If m times the mth term is equal to n times the nth term of an A.P. pr...

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  6. Find the sum of indicated number of terms of the following A.P.’s : ...

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  7. Find the sum of indicated number of terms of the following A.P.’s : ...

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  8. Find the sum of indicated number of terms of the following A.P.’s : ...

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  9. Find the sum of indicated number of terms of the following A.P.’s : ...

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  10. Find the sum of indicated number of terms of the following A.P.’s : ...

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  11. Out of k, a, n, d and Sn, determine the ones that are missing from the...

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  12. Out of l, a, n, d and Sn, determine the ones that are missing from the...

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  13. How many terms of the sequence 18, 16, 14.... should be taken so that ...

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  14. How many terms of the sequence -12,-9, -6, -3, ..... must be taken to ...

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  15. How many terms of the sequence -6,(-11)/2, -5,.... must be taken to ma...

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  16. Find the sum of the series : 72 + 70 + 68 +....+ 40?

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  17. Find the sum of first n natural numbers.

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  18. Find the sum of first 100 natural numbers.

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  19. Find the sum to n terms of the A.P. whose kth term is 5k + 1.

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  20. If the sum of n terms of an A.P. is (pn+qn^2), where p and g are const...

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