The value of the expression `1-((n/1).((1+x)/(1+nx))+((n(n-1))/(1.2))((1+2x)/(1+nx)^2)-((n(n-1)(n-2))/(1.2.3))((1+3x)/(1+nx)^3)...`

Prove that 1-^(n)C_(1)(1+x)/(1+nx)+^(n)C_(2)(1+2x)/((1+nx)^(2))-^(n)C_(3)(1+3x)/((1+nx)^(3))+

If f(x)=1+nx+(n(n-1))/2x^(2)+(n(n-1)(n-2))/6x^(3)+………………+x^(n), then f^(")(1)=

Sum to n terms of the series (1)/((1+x)(1+2x))+(1)/((1+2x)(1+3x))+(1)/((1+3x)(1+4x))+ is (i) (1+x)(1+nx)((1+x)(1+nx))/((1+x)(1+(n-1)x))( iv )((1+x)(1+(n+1)x))/((1+x)(1+(n+1)x))

The value of lim_(x rarr oo)(2x^((1)/(2))+3x^((1)/(3))+4x^((1)/(4))+......+nx^((1)/(n)))/((2x-3)^((1)/(2))+(2x-3)^((1)/(3))+......+(2x-3)^((1)/(n))) is equal to

Show that: (x)+(x+(1)/(n))+(x+(2)/(n))+...+(x+(n-1)/(n))=nx+(n-1)/(2)

int(e^(x)(1-nx^(n-1)-x^(2n)))/((1-x^(n)) sqrt(1-x^(2n)))d=....+c

Evaluate: lim_(n rarr oo)((a_(1)^((1)/(1))+a_(2)^((1)/(2))+...+a_(n)^((1)/(n)))/(n))^(nx)

The value of lim_(x rarr0)((e^(1))/(x))-(1+nx+(n^(2))/(2)x^(2))/(x^(3))(n>0) is

If (n^(n))/(n!)=(nx)/((n-1)!), x =