Find (i) the `n^(th)` term and (ii) the sum of first n terms of the series `6+15x+28x^2+45x^3+...`

Find the sum to n terms of the series: 1+2x+3x^(2)+4x^(3)+......

The nth term of a series is 3^(n)+2n; find the sum of first n terms of the series.

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

The nth term of a series is 3^n + 2n ; find the sum of first n terms of the series.

Find the sum of n terms of the series (x+y)+(x^(2)+2y)+(x^(3)+3y)+...

Find the sum of n terms of the series (x+y)+(x^(2)+2y)+(x^(3)+3y)+...