Sum of the following series `1+2/2+3/(2^2)+4/(2^3)+...` to n terms

Find the sum of the following series : 1.2+2.3+3.4+ .... to n terms .

Find the sum of the following series : 3.1^2+5.2^2+7.3^2 + .... to n terms .

Sum of the following series (i) 1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+ ……..to n terms (ii) 1+(3)/(4)+(7)/(16)+(15)/(64)+(31)/(256)+………. to infinity.

Find the sum to n terms of the following series : 1+2/3 +3/3^2+4/3^3 + .......

Find the sum to n terms of the following series : 1+3/2+5/2^2+7/2^3 + ...........

Find the sum to n terms of the following series : 1+2a + 3 a^(2) + 4a^(3) + …, [a != 1]

Find the sum to n terms of the following (1-2) series: (i) 1+3/2+5/(2^(2))+7/(2^(3))+ ………….. (ii) 1+2/3+3/(3^(2))+4/(3^(3))+ …………

Find the sum to n terms of each of the following series : 1^(2) - 2^(2)+3^(2) - 4^(2) + 5^(2) - 6^(2)+…