Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

Question

∑n=1 to ∞

5^n+1 * 6^-n

Answer 1

(5ⁿ⁺¹)(6^-n) = 5(5ⁿ)/6ⁿ = 5(5/6)ⁿ

So, the given series is equivalent to 5∑_{n=1 to ∞}(5/6)ⁿ = 5[(5/6) / (1 - 5/6)] = (5)(5) = 25

Answer 2

a_n = 25 / 6

r = 5 / 6

Use formula for sum of infinite geometric series.