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26-05-2020
Mathematics

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

State why the series is convergent or divergent and if it is convergent find the sum class=

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MathPhys MathPhys

26-05-2020

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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