Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.......

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) =-prod_(r=1)^(n) (1- n ^(r))`

`f (x)=1 -prod_(r =1)^(n)(1- x ^(r))`

`f (x) =(1 =f (x)) (prod _(r =1)^(n)(r x ^(r-1))/((1-x ^(r ))))`

`f '(x) =f (x) ((prod _(r =1) ^(n) (r x ^(r-4))/((1- x^(r))))`

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