Question

State why the series is convergent or divergent, and if it is convergent, find the sum.

Answer 1

Converges, 10

Explanation:

∑ 5 / 2ⁿ⁻¹

= ∑ 5 (½)ⁿ⁻¹

This is a geometric series with a₁ = 5 and r = ½. Since |r| < 1, the series converges to:

S = a₁ / (1 − r)

S = 5 / (1 − ½)

S = 10