Let `f(x)=x+(1-x)x^2+(1-x)(1-x^2)x^3+.............+(1-x)(1-x^2)..........(1-x^(n-1))x^n;(n >= 4)` then :

Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x^(n-1))x^n;(n >= 4) then :

Let f(x)=x+(1-x)x^(2)+(1-x)(1-x^(2))x^(3)+............+(1-x)(1-x^(2)).........(1-x^(n-1))x^(n);(n) then :

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

f(x)=lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))..........(1+x^(2^(n-1))) then

Let f(x)=(1-x^(n+1))/(1-x) and g(x)=1-(2)/(x)+(3)/(x^(2))-...+(-1)^(n)(n+1)/(x^(n)) Then the constant term in f'(x)xx g(x) is equal to -

Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) (1-3x)............[1-(n-1)x].

Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) (1-3x)............[1-(n-1)x].

Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+...+n(1-x)(1-2x)(1-3x)...[1-(n-1)x

Let P_(n)=((1+x)(1-x^(2))(1+x^(3))(1-x^(4)))/({(1+x)(1-x^(2))(1+x^(3))(1-x^(4))(1-x^(2n))}^(2)) Let Prove that the term independent of x in the expansion of (x^(2)+(1)/(x^(2))+2)^(2n) is equal to lim_(x rarr-1)Pn.