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If a1, a2, a3…..an are in AP, then prove...

If `a_1, a_2, a_3`…..`a_n` are in AP, then prove that `frac(1)(a_1 a_2)+frac(1)(a_2 a_3)+frac(1)(a_3 a_4)+.....+frac(1)(a_(n-1) a_n)=frac(n-1)(a_1 a_n)`

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KALYANI PUBLICATION-PROGRESSION-EXERCISE
  1. There are p A.M.'s between 5 and 41 and third mean : (p-1)th mean = 2 ...

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  2. The product of two numbers is 16. The product of two A.M.’s between th...

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  3. If a1, a2, a3…..an are in AP, then prove that frac(1)(a1 a2)+frac(1)(a...

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  4. Find the sum of the following series up to the specified term 1 + ...

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  5. Find the sum of the following AP up to the specified term 2 + 6 + ...

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  6. Find the sum of the following AP up to the specified term 20+ 18+ ...

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  7. Find the sum of the following AP is up to the specified term 4+7+1...

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  8. Find the sum of the following AP up to the specified term 1/2+1/3+...

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  9. Find the sum of the following series up to the specified term sqrt...

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  10. Find the sum of the following series up to the specified term -8-3...

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  11. Find the sum of the following series up to the specified term (x^2...

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  12. Find the sum of the following series up to the specified term (x-...

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  13. Find the sum of the following series up to the specified term n/n+...

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  14. Find the sum of the following series up to the specified term 1 + ...

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  15. Find the sum of the following series up to the specified term 2+5+...

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  16. Find the sum of the following series up to the specified term 1-3-...

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  17. By inserting eight A.M.’s between 2 and 29 prove that the sum of t...

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  18. Show that the sum of 500 A.M.’s between 2 and 3 is 1250.

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  19. Prove that the ratio of the sum of m A.M.’s between any two n...

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  20. The sum of fIrst n terms of an A.P series is 26n-2n^2. Find the fifth ...

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