[" to infinite series "],[1+3(1-(1)/(x))+5(1-(1)/(x))^(2)+7(1-(1)/(x))^(3)+...],[" is "2x^(2)-x],[" Statement-2: If "0

Statement -1: If xgt1 , the sum to infinite series 1+3(1-(1)/(x))+(1-(1)/(x))^(2)+7(1-(1)/(x))^(3)+ . . . .," is "x^(2)-x Statement -2: If 0ltylt1 , the sum of the series 1+3y+5y^(2)+7y^(3)+ . . . .," is "(1+y)/((1-y)^(2))

For x>0 the sum of the series (1)/(1+x)-(1-x)/((1+x)^(2))+((1-x)^(2))/((1+x)^(3))-...oo is equal to

The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/(x+1)^(2)+1/3(x^(3)-1)/(x+1)^(3) +…is equal to

Then sum of the series 1+(1|3)/(2!)x+(1|3|5)/(3!)x^(2)+(1+3+5+7)/(4!)x^(3) x+…is

Then sum of the series 1+(1+3)/(2!)x+(1+3+5)/(3!)x^(2)+(1+3+5+7)/(4!)x^(3) x+…is

Solve for : :(3)/(x+1)-(1)/(2)=(2)/(3x-1),x!=(3)/(5),-(1)/(7)

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