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If `a_n` denotes the coefficient of `x^n` in P(x) =` (1 + x+ 2x^2 + 3x^3 +... + n x^n)^2`. then the last digit of `a_24` must be

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

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  2. A three digit number whose consecutive digits from a G.P. If we subtra...

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  3. If an denotes the coefficient of x^n in P(x) = (1 + x+ 2x^2 + 3x^3 +.....

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  4. Two consecutive numbers from 1,2,3,.....,n are removed, then arithmeti...

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  5. The value of xyz is 55 or 343/55 according as the sequence a, x, y, z,...

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  6. If a, b, c are in HP and if ((a + b)/(2a - b)) + ((c + b)/(2c - b)) gt...

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  7. If alpha1 , alpha2, ......, alphan are in A.P, whose common difference...

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  8. 25 trees are plants in a straight line 5 metre apart from each other. ...

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  9. The nth term of a series is given by tn = (n^5 + n^5)/(n^4 + n^2 + 1) ...

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  10. If a1. a2 ....... an are positive and (n - 1) s = a1 + a2 +.....+an th...

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  11. Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2...

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

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

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

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

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

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

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

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

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

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