Find the sum of the infinite geometric series.

Question

Σ(n=0 to infinity) -3(-1/5)ⁿ

Please show your work. Thx

Answer 1

Σ^∞₀ -3(1/5)ⁿ

This is the sum of an infinite geometric series. Geometric because each term is (1/5) smaller than the one before it. For example, the 0th term is -3 and the 1st term is -3(1/5).

We must remember that

Σ^∞₀ a(r)ⁿ = a/(1-r) only if r makes the next term smaller.

In other words the sum is a simple formula, but only if r is strictly between -1 and 1 and not 0.

1/5 is a suitable r value to use in the formula so the answer is only a matter of simplifying a compound fraction.