श्रेणी के n पदों तक योगफल निकालिए।
`1^(2)/1+(1^(2)+2^(2))/(1+2)+(1^(2)+2^(2)+3^(2))/(1+2+3)+...`

(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1+ 2+ 3)+ …. + n terms =

The sum of 1^(st) n terms of the series (1^(2))/(1) + (1^(2) + 2^(2))/(1 + 2) + (1^(2) + 2^(2) + 3^(2))/(1 + 2 + 3) + ..

1^(3) + 1^(2) + 1+2^(3) + 2^(2) + 2+3^(2) + 3^(2) + 3+3… 3n terms =

Find 1^2/1 + (1^2 + 2^2) / 2 + (1^2 + 2^2 + 3^2) / 3 + …..upto n terms.

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2)+2^(2))/(1^(3)+2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

1+(1)/(1+2)+(1)/(1+2+3)+(1)/(1+2+3+n)=(2n)/(n+1)

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2))/(1^(3))+(2^(2))/(2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

(1)/(2n^(2)-1)+(1)/(3(2n^(2)-1)^(3))+(1)/(5(2n^(2)-1)^(5))+....=

The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3^(2))//(3.4!)+..+(1^(2)+2^(2)+…+n^(2))/(n.(n+1))!+..infty is equals to