`x gt0`, then the sum of the series `e^(-x)-e^(-2x)+e^(-3x)-...` i s

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

If x gt 0 then the sum of the series e^(-x) - e^(-2x) + e^(-3x) ......infty is

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

The sum of the series 1+2x+3x^(2)+4x^(3)+... upto infinity when x lies between 0 and 1 i.e.,0

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)

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 number of real solutions of the equation, e^(4x)+e^(3x)-4e^(2x)+e^(x)+1=0 is

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

The number of real roots of the equation e^(6x)-e^(4x)-2e^(3x)-12e^(2x)+e^(x)+1=0 is :

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