What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-half) Superscript n minus 1

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asked Sep 15, 2021 38.3k views

2 Answers

Rohit Parte · Answer 1 · 2021-09-19T09:33:10+0000

Explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = -144, and r = ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288