1.

Find the sum of n terms of the series whose nth term is: `n^3-3^n`

Answer» Correct Answer - `(1)/(4)n^(2)(n+1)^(2)-(3)/(2)(3^(n)-1)`
`T_(n)=(n^(3)-3^(n)). `
`because S_(n)=(sum_(k=1)^(n)k^(3))-(sum_(k=1)^(n)3^(k))=(1)/(4)n^(2)(n+1)^(2)-{3+3^(2)+...+3^(n)}`
`rArr S_(n) ={(1)/(4)n^(2)(n+1)^(2)-(3(3^(n)-1))/((3-1))}`.


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