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

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

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RD SHARMA ENGLISH-SOME SPECIAL SERIES-All Questions
  1. If Sk=(1+2+ ..........+k)/k , find the value of S1^2+S2^2+.........+S ...

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  2. Find the sum of n terms of the series 1. 2^2+2. 3^2+3. 4^2+

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

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  4. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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