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Prove that the sum of n arithmatic means...

Prove that the sum of n arithmatic means between two numbers is n times the single A.M between them.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If a,b,c be in H.P prove that (1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2

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  2. If a,b,c are in H.P. show that a/(b+c),b/(c+a),c/(a+b) are also in H.P...

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  3. Prove that the sum of n arithmatic means between two numbers is n time...

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  4. Find the sum to n terms of the series: 5+11+19+29+41.....

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  5. Find the sum of n terms of the series 3+7+14+24+37+.....

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

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

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

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

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

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  11. 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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  12. 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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  13. Find the sum of 2.3+3.4+4.5+......to n terms.

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

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

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

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

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

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

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

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