Find the sum of n-terms of the following series:`(x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)^2+(x^4+1/x^4)^2+...`

The sum of 10 terms of the series (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)^2+.... is

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

Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1//x)^2 , ....

Find the sum to infinity of the series 1^2+2^2x+3^2x^2+oodot

Find the middle term (or terms) in the following expansions: (iv) (2x-1/(3x))^(2n)

Find the sum of the series : 1^(2) + 2^(2)x + 3^(2)x^(2) + 4^(2) x^(3)+…. oo

sum_(r=1)^ntan^-1((x_r-x_(r-1))/(1+x_(r-1)x_r))=sum_(r=1)^n(tan^-1x_r-tan^-1x_(r-1))=tan^-1x_n-tan^-1x_0, AAn in N Answer the following question on above passage: The sum to infinite terms of the series cot^-1(2^2+1/2)+cot^-1(2^3+1/2^2)+cot^-1(2^4+1/2^3)+ ..... is

If f(x)=(1)/(x^(2)) , show that f(x)-f(x+1)=(2m-1)/(x^(2)(x+1)^(2)) , hence find the the sum of first n terms of the series (3)/(1^(2)*2^(2))+(5)/(2^(2)*3^(2))+(7)/(3^(3)*4^(2))+....

Find the term independent of x in each of the following expansions : ((3)/(2)x^(2)-(1)/(3x))^(12)

Find the sum of the series 1-3x+5x^2-7x^3+ ton terms.