Sum the series `x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3)+` upto n terms, `x^2 ne 1, xy ne 1`

Verify : x^3-y^3=(x-y)(x^2+xy+y^2) .

Verify : x^3+y^3=(x+y)(x^2-xy+y^2) .

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

Find the sums of the indicated number of terms of the following geometric progressions : x^2-y^2,x-y, (x-y)/(x+y) , ...., n terms (x+y ne 1) .

If x and y be real, show that the equation : sin^2 theta= (x^2+y^2)/(2xy) is possible only when x =y ne 0 .

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2, then

If |x|<1 and |y|<1, find the sum to infinity of the series : (x+y)+(x^2+x y+y^2)+(x^3+x^2y+x y^2+y^3)+ .......