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Prove that sum(n=1)^infty n/(4n^4+1) equ...

Prove that `sum_(n=1)^infty n/(4n^4+1)` equals to `1/4`.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find the sum of n terms of the series 3+7+14+24+37+.....

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  2. Find the sum of series 3+8+22+72+266+1036+....

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  3. Prove that sum(n=1)^infty n/(4n^4+1) equals to 1/4.

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  4. Prove that sum(n=1)^infty n/(4n^4+1) equals to 1/4.

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  5. Show that the sum of sum(n=1)^infty n/(n^4+4) equals to 3/8

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  6. Show that the sum of sum(n=1)^infty n/(n^4+4) equals to 3/8

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  7. Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2...

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  8. Find the sum of the series 1/(1.2.3.4)+1/(2.3.4.5)+1/(3.4.5.6)+..........

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  9. Find the sum of 2.3+3.4+4.5+......to n terms.

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  10. If a,b,c are positive real no., then prove that [(1+a)(1+b)(1+c)]^7 g...

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  11. If a,b,c are the sides of a triangle and s=(a+b+c)/2 , prove that 8(s-...

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  12. Prove that a^4+b^4+c^4>abc(a+b+c). [a,b,c are distinct positive real n...

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  13. Show that the greatest value of xyz(d-ax-by-cz) is d^4/(4^4abc).

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  14. Prove that ((a+b)/2)^(a+b) le a^a.b^b.[a,binN].

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  15. N arithmetic means are inserted in between x and 2y and then between 2...

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  16. Let Sn denote the sum upto n terms of an AP . If Sn=n^2P and Sm=m^2P ...

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  17. If s1 ,s2 and s3 are the sum of first n,2n,3n terms respectively of an...

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  18. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

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  19. A G.P. consists of 2n terms . If the sum of the terms occupying the od...

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  20. If G1 ,G2 are geometric means , and A is the arithmetic mean between ...

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