`sum_(n=0)^oo (-1)^n x^(n+1)=`

Let x= sum_(n=0)^oo (-1)^n (tantheta)^(2n) and y = sum_(n=0)^oo (costheta)^(2n) qhere theta in (0,pi/4) , then

Let x= sum_(n=0)^oo (-1)^n (tantheta)^(2n) and y = sum_(n=0)^oo (costheta)^(2n) qhere theta in (0,pi/4) , then

For x in Rwith|x|<1, the value of sum_(n=0)^(oo)(1+n)x^(n) is

sum_(n=0)^(oo) (n^(2) + n + 1)/((n +1)!) is equal to

sum_(n=1)^(oo)(1)/(2n(2n+1))=

sum_ (n = 0) ^ (oo) (1) / (n!) [sum_ (k = 0) ^ (n) (i + 1) int_ (0) ^ (1) 2 ^ (- (k + 1 ) x) dx]

Given x in(-1,0)uu(0,1) and f(x)=sum_(n=0)^(oo)x^(n)(-1)^((n(n+1))/(2)) The function f(x) is equivalent to a rational function