Show that `1+(1+3)/(2!)+(1+3+3^2)/(3!)+...=1/2(e^3-e)`

Show that 2(1/(3!)+2/(5!)+3/(7!)+...)=1/e

Show that 1.3/(1!)+2.4/(2!)+3.5/(3!)+4.6/(4!)+...=4e

Show that 9/(1!)+19/(2!)+35/(3!)+57/(4!)+85/(5!)+...=12e-5

Show that 1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...=sqrte-1

Show that 2 tan^-1(1/4) + 2 tan^-1 (2/9) = tan^-1(4/3) .

Show that C_1^2 + 2C_2^2 + 3(3^2 + ... + "^nC_n^2 = ((2n-1!))/{(n-1)!}^2

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

Show that the points (1,2,3), (2,3,1) and (3,1,2) from an equilateral triangle.

Show that C_2 + 2C_3 + 3C_4 + ... + (n-1)C_n = 1+ (n-2) 2^(n-1)