Find the sum of `n` terms of the series `1. 2^2=2. 3^2+3. 4^2+`

Find the sum of n terms of the series 1^3+3.2^2+3^3+3.4^2+5^3+3.6^2+....... when (i)n is odd (ii)n is even

Find the sum to n terms of the series 1.2.3+2.3.4+3.4.5+…

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

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+...............+1/(n.(n+1))

Find the nth term and the sum of n terms of the series 1.2.4+2.3.5+3.4.6+....

Find the sum to n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...

(2a^(2)-1)/(n),4a-(3)/(a),(6a^(2)-5)/(a)15. Find the sum of n terms of the series,36a- 5

Find the sum of first n terms of the series 3/(1^(2).2^(2))+5/(2^(2).3^(2))+7/(3^(2).4^(2))+.......+ and deduce the sum of infinity .