If `|x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+......` is equal to a.`((2x)/(1+x))^n` b. `((1+x)/(2x))^n` c. `((1-x)/(1+x))^n` d. `((1+x)/(1-x))^n`

If |x|<1 then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+......oo

If |x|lt(1)/(2), what is the value of 1+[(x)/(1-x)]+[(n(n+1))/(2!)][(x)/(1-x)]^(2)+............+oo ?

The sum of 1+n(1-(1)/(x))+(n(n+1))/(2!)(1-(1)/(x))^(2)+...oo will be x^(n) b.x^(-n) c.(1-(1)/(x))^(n) d.none of these

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

if |x|<1 then (Lt)_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))......*(1+x^(2n))=

If x+1/x=-2 then x^(2n+1)+1/(x)^(2n+1)=

cos^(-1)((1-x^(2n))/(1+x^(2n)))

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

If f(x) =1 + nx+ (n(n-1))/(2) x^(2) + (n(n-1)(n-2))/(6) x^(3) + ...+ n^(x) , "then" f''(1) is equal to

If x_(1)=1 and x_(n+1)=(1)/(x_(n))(sqrt(1+x_(n)^(2))-1),n>= then x_(n) is equal to