Geometric Series Sandbox

MTH-117 · Semester I · Mathematics I

Sum of a geometric series

Guided practice — solve each problem, check, then generate a fresh one.

Score 0 / 0

Formula to apply

Σₙ₌₀^∞ a·rⁿ = a/(1 − r), |r| < 1

Problem

Find the sum of the infinite geometric series 5 + 1.25 + 0.3125 + … (first term 5, ratio 0.25).

Working

  1. 1|r| = 0.25 < 1, so the series converges.
  2. 2S = a/(1 − r) = 5/(1 − 0.25).
  3. 3S = 5/0.75 = 6.6667.