The sum of the series `x/(1)+(2x^2)/(2)+(3x^3)/(3)+` is `x e^x` b. `-x e^x` c.`x e^x-x` d. `x e^x+x`

x>0, then the sum of the series e^(-x)-e^(-2x)+e^(-3x)-... is

Find the sum of the series e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...

Statement -1: The sum of the series (1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)+..to infty is e Statement 2: The sum of the seies (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(4)/(4!)x^(4)..to infty is x e^(x)

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)

The inverse of the function f(x)=(e^(x)-2e^(-x))/(e^(x)+2e^(-x))+1 is

The number of solution of the equation e^(2x)+e^(x)+e^(-2x)+e^(-x)=3(e^(-2x)+e^(x))

The value of lim_(x rarr0)((1+2x)/(1+3x))^((1)/(x^(2)))*e^((1)/(x)) is e^((5)/(2))b.e^(2)ce^(-2)d.1

y = e ^ (2x) + e ^ (3x)

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

(dy)/(dx) =y ((e^(3x)-e^(-3x))/(e^(3x) +e^(-3x)))