InterviewSolution
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InterviewSolution
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Find the sum of the following series up to n terms : `(1^3)/1+(1^3+2^2)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+dotdotdot` |
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Answer» `r^(th)` term in the given expression can be given as, `T_r = (1^3+2^3+3^3+...)/(1+3+5+...)` `=>T_r = (((r(r+1)))/2)^2/(r^2)` `=>T_r = (r^2(r+1)^2)/(4r^2)` `=>T_r = 1/4(r+1)^2` `=>T_r = 1/4(r^2+1+2r)` `:.` Sum of given series ` = sum T_n = 1/4 (sum n^2+ sum 1 + sum 2n)` `= 1/4[(n(n+1)(n+2))/6+n+2*(n(n+1))/2]` `=n/4[((n+1)(n+2))/6+(n+2)]` |
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