Summation Problem: Find Sum of 3r - 2r to n Terms

[lionely]

Homework Statement

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

Homework Equations

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]

Homework Statement

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

Homework Equations

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

 

[lionely]

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

 

[Mark44]

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.