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If the sum of m terms of an AP is equal ...

If the sum of m terms of an AP is equal to the sum of either the next n terms or the next p terms, then prove that `(mn)((1)/(m)-(1)/(p))=(m+p)((1)/(m)-(1)/(n))`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
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  12. If b^2+c^2, c^2+a^2, a^2+b^2 are in A.P. prove that : 1/(b + c), 1/(c...

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  13. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(...

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  14. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

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  15. If the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  16. If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2).

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  17. If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b,...

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  18. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

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  19. If x,y,z are in G.P. and a^x= b^y=c^z, prove that logb a. logb c=1.

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  20. We are given two G.P.'s, one with the first term 'a' and common ratio ...

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