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Evaluate, sum(i = 0)^iinfty sum(j = 0)^i...

Evaluate, `sum_(i = 0)^iinfty sum_(j = 0)^infty sum_(k = 0)^infty 1/(3^i cdot 3^j cdot 3^k) ( i ne j ne k)`

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2...

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  2. Evaluate , S =sum(n = 0)^infty 2^n/(a^(2^n) + 1) (where a gt 1)

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  3. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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

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

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

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

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

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

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

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  11. Let d(n) denotes the number of divisors of n including 1 and itself. T...

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  12. Let a, b , c be positive integers such that b/a is an integer. if a, b...

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  13. If (10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+..+10(11)^9 = k(10)^9 then...

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  14. Three positive numbers from an increasing G.P. If the middle term in t...

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

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

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

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

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  20. The value of 1000[1/(1 xx 2) + 1/(2 xx 3) + .........+1/(999 xx 1000)]...

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