∑(n=1)^∞ /(5^n)
Determine whether the series converges, and if it converges, determine its value
= (3/5) * ∑(n=1)^∞ : (1/5)^(n-1)
This is a multiple of the geometric series with |r| = 1/5 < 1.
So, the sum equals (3/5) * [1/ (1 - 1/5)] = 3/4.
I hope this helps!
/(5^n)
Comments
∑(n=1)^∞
/(5^n)
= (3/5) * ∑(n=1)^∞ : (1/5)^(n-1)
This is a multiple of the geometric series with |r| = 1/5 < 1.
So, the sum equals (3/5) * [1/ (1 - 1/5)] = 3/4.
I hope this helps!