Sequence of 3/4^(2k). Show is convergent, find sum

[939]

Homework Statement

Consider the sequence ak = (3)/(4^(2k)). Show is convergent, find sum. Please check work.

Homework Equations

ak = 3/(4^2k)

let s {n} be the series associated with the sequence. Cannot write summation notation here, but k starts at 1 (k = 1 on bottom) and infinity on top.

The Attempt at a Solution

ak1 = 0.1875
ak2 = 0.01171875
ak3 = 0.000732421876
ak4 = 0.00004577636719

ak4/ak3 = 0.0625

Convergence: 1) r = 0.0625. r < 1, ∴ convergent
Sum: 2) (0.1875)/(1-0.0625) = 0.2. Sum is 0.2

 

[ehild]

It is correct, if the summation starts with k=1.

ehild

 

[939]

It is correct, if the summation starts with k=1.

ehild

Thanks! Yes, it does.