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1+(1/3+1/(3^2))+(1/(3^3)+1/(3^4)+1/(3^5)...

`1+(1/3+1/(3^2))+(1/(3^3)+1/(3^4)+1/(3^5))+.....` sum of the terms in the `n^(th)` bracket=

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The sum of series 1/(1-3.1^2+1^4)+2/(1-3.3^2+2^4)+3/(1-3.3^2+3^4)+......... up to 10 terms, is equal to

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Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2)+2^(2))/(1^(3)+2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

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FIn dthe sum of this series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)+(1^(3)+2^(3)+3^(3))/(1+3+5)+...+ till 10^(th) term ^(*)

For the series, S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7))(1+2+3+4)^2 +... a.7th term is 16 b.7th term is 18 c. Sum of first 10 terms is (505)/4 d. Sum of first 10 terms is (45)/4

The sum of (3)/(1.2)*(1)/(2)+(4)/(2.3)*((1)/(2))^(2)+(5)/(3.4)*((1)/(2))^(3)+ to n terms is equal to