# Summation problem

## Homework Statement

Find the sum to n terms of the series whose rth term is 3r - 2r

## The Attempt at a Solution

So I tried this

rlog3 - rlog2 = n(n+1)/2 log3 - n(n+1)/2 log2

then I realized this was kind of useless, the only thing I could get from this is

n(n+1)/2 log (3/2) , then I don't know what to do with it.

the answer in the book is 3n+1/2 -2n+1 + 1/2

Mark44
Mentor

## Homework Statement

Find the sum to n terms of the series whose rth term is 3r - 2r

## The Attempt at a Solution

So I tried this

rlog3 - rlog2 = n(n+1)/2 log3 - n(n+1)/2 log2
You have a mistake right off the bat. log(A - B) ≠ logA - logB.
Split your series into two - each part is a geometric series.
then I realized this was kind of useless, the only thing I could get from this is

n(n+1)/2 log (3/2) , then I don't know what to do with it.

the answer in the book is 3n+1/2 -2n+1 + 1/2

I see it now thanks.. I keep making those darned mistakes with logs!!

Mark44
Mentor
It would be worth your while to review the properties of logs. They might be listed in an appendix of the book you're using. If not, get a precalc book or put in some time in an online tutorial such as khanacademy or the like.