Series

[exotic spindle]

4^b = (2•2)^b or 2^b • 2^b
8^b = (4•2)^b = 4^b • 2^b
This is just a geometric series with common ratio 2^b

[proven lodge]

@exotic spindle so how does that help solve for b? The problem is asking for a value of b such that the series given equals 16/15

[exotic spindle]

Do you remember the formula for sum of infinite geometric series

[proven lodge]

@exotic spindle could you enlighten me?

[exotic spindle]

For a infinite geometric series the sum is
A/(1-r) where A is first term and r is common difference
Solve 1/(1-r) = 16/15 to get your common ratio

Then r=2^b to get b

[proven lodge]

@exotic spindle then just do some algebra to solve for b?

[exotic spindle]

Yea