Sum the series upto n terms, also find sum when`n to oo`.
`(3)/(2^(3))+(4)/(2^(4).3)+(5)/(2^(6).3)+(6)/(2^(7).5)+…….`

The sum of the series 1+ 2/3+ (1)/(3 ^(2)) + (2 )/(3 ^(3)) + (1)/(3 ^(4)) + (2)/(3 ^(5)) + (1)/(3 ^(6))+ (2)/(3 ^(7))+ …… upto infinite terms is equal to :

Find the sum of: 24 terms and n terms of 2 (1)/(2) , 3 (1)/(3) , 4 (1)/(6) ,5 ,......,

Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6) + (7)/(2.4.6.8)+ (9)/(2.4.6.8.10)+……

Sum of the n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(3))+"......." is

Sum up to n terms of series (1)/(2)+(3)/(6)+(5)/(18) + ...

Find the sum to n terms of the series whose nth term is 4n^(3)+6n^(2)+2n

Sum to n terms of the series 1^(3) - (1.5)^(3) +2^(3)-(2.5)^(3) +…. is

Sum to n terms the series (3)/(1 ^(2) . 2 ^(2)) + (5)/( 2 ^(2) . 3 ^(2)) + (7)/( 3 ^(2) . 4 ^(2)) +.............

Find the sum of n terms of the series whose n t h term is: 2n^2-3n+5

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sum of different series. Q. Sum of infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo is