Math Question

[mollymvora]

if abs(x) < 1, find the sum S of the series 1 + 2x + 3x^2 + 4x^3 ....... (Hint: Consider S - xS)

I can see the geometric matter in the variables, but what about the coefficients?

 

[Deleted member 4993]

if abs(x) < 1, find the sum S of the series 1 + 2x + 3x^2 + 4x^3 ....... (Hint: Consider S - xS)

I can see the geometric matter in the variables, but what about the coefficients?

S = 1 + 2x + 3x^2 + 4x^3 ......

Sx =      x + 2x^2 + 3x^3......

(S-Sx) = 1 + x + x^2 + x^3.......

All the coefficients are gone now......