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

Mathematics

1 answer:

MatroZZZ [7]3 years ago

8 0

Answer:

Converges, 10

Step-by-step 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

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