Question

If |x| < 1. Find the sum to infinity of the series $3 + 8x + 13x^2 + 18x^3 + ----- \infty$

• A. $(3+2x)/(1-x^2)$
• B. $(3-2x)/(1+x^2)$
• C. $(2x-3)/(1-x^2)$
• D. $(3+2x)/(1+x^2)$

 

Answer 1

Series, S  = $3 + 8x + 13x^2 + 18x^3 + ------\infty$  → Eq (1)

            xS = $3x + 8x^2 + 13x^3 + 18x^4 + ------\infty$  → Eq(2)

Let us subtract Eq (2) from Eq(1) [1 – 2]

S – xS = 3 + [ 5x + $5x^2 + 5x^3 + ------ \infty $

S [1 – x] = 3 + 5 [ x + $x + x^2 + x^3 + ----- \infty $

Infinite series, $(a/1-r)$

= S [1-x] = 3 + 2x and S = $(3+2x)/(1-2x^2)$