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If a, b, c, d are four distinct numbers in A.P. , show that `1/a + 1/d gt 1/b + 1/c gt 4/(a + d)`

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  2. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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  3. If a, b, c, d are four distinct numbers in A.P. , show that 1/a + 1/d ...

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  4. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

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  5. Let the harmonic mean of two positive real numbers a and b be 4. If q ...

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  6. Suppose that all the terms of an arithmetic progression (A.P) are natu...

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  7. The sum of first 9 terms of the series 1^3/1 + (1^3 + 2^3)/(1 + 3) + (...

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  8. If m is the A.M. of two distinct real number l and n(l , n gt 1) and G...

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  9. If sin^-1 ( x-x^2/2 + x^3/4 - x^4/8 +....) = pi/6 where absx lt 2 then...

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  14. Let f(x) = x + 1/2 , then the number of real values of x for which the...

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  15. If a, b and c are positive numbers in a G.P., then the roots of the qu...

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  16. The minimum value of 2^(sin x) + 2^(cos x) is

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  17. If x, y , z are in A.P and tan^-1 x , tan^-1 y and tan^-1 z are also ...

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  18. The sum of first 20 terms of the sequence 0.7 , 0.77 , 0.777,... is

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  20. Let f : R rarr R be such that f is is injective and f(x) f(y) = f(x + ...

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