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# Sum of first n terms of a geometric series ? 1 + 2 + 2^2 +...+ 2^n-1 + 2^n watch

1. I typed it incorrectly in the title

The Series is 1 + 2 + 2^2 +...+ 2^n-1 + 2^n

How do I find the sum of the above series ?
2. (Original post by James222)
I typed it incorrectly in the title

The Series is 1 + 2 + 2^2 +...+ 2^n-1 + 2^n

How do I find the sum of the above series ?
This is a GP and so the standard formula applies, as your first term is 1.
a=1, r=2

So, as an example-test, for the first 4 terms, n=4
Which is 1+2+4+8.
3. (Original post by nerak99)
This is a GP and so the standard formula applies, as your first term is 1.
a=1, r=2

So, as an example-test, for the first 4 terms, n=4
Which is 1+2+4+8.
Thanks but my textbook has the following answer http://imgur.com/a/xke9G

Any idea why they have r^n+1 rather than just r^n ?
4. Not really. If you put in t=1 into their formula for yt, you get y1=3 ?
5. (Original post by nerak99)
Not really. If you put in t=1 into their formula for yt, you get y1=3 ?
Perhaps they have a different formula?
6. There are n+1 terms in the sequence, Therfore
7. On the face of it maths and chess is right. However In the scan they refer to 1 as the first term, not the zeroeth. Thus the nth term is 2^(n-1). Then in the formula for yt they seem to count from 0. I think it is the text that is not clear.

To compound the confusion they then quote the formula that I used.

The usually quoted formula is for the sum to n terms.

However, please clear up my confusion.

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