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Prove that :1^2+2^2+3^2++n^2=(n(n+1)(2n+...

Prove that :`1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6`

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RD SHARMA ENGLISH-SOME SPECIAL SERIES-All Questions
  1. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

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  2. Prove that :1^3+2^3+3^3++n^3={(n(n+1))/2}^2dot

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  3. Prove that :1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

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  4. Find the sum of the series 2^2+4^2+6^2++(2n)^2

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  5. Find the sum of nth term of this series and Sn denote the sum of its n...

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  6. Sum the following series to n terms: 1/(1. 6)+1/(6. 11)+1/(11. 16)+1/(...

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  7. Sum the following series to n terms: 1+4+13+40+121+

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  8. Find the sum of all possible products of the first n natural numbers t...

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  9. Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+....

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

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  11. Sum the following series to n terms: 4+6+9+13+18+

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  12. Find the sum : sum(r=1)^n1/((a r+b)(a r+a+b))

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

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  14. Sum the following series to n terms: 5+7+13+31+85+

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  15. Find the sum to n terms of the series: 1/(1. 3)+1/(3. 5)+1/(5. 7)+

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  16. Find the sum to n terms of the series: 3+15+35+63+

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  17. Find the sum to n terms of the series: 1+5+12+22+35+........

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  18. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

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  19. Find the sum of series (3^3-2^3)+(5^3-4^3)+(7^3-6^3)+... n terms.

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  20. If Sn=sum(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then Sn is equal to (a)2...

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