# Calculate the sum of the first N terms of the sequence

$a_n=a_{n-1}\displaystyle \frac{n+1}{n}$ if $n > 1$

$a_n=1$ if $n=1$

I'm not too sure where to start here. This is part of a review for a class and I can't really seem to remember what we're reviewing. The first 5 values are...

$a_1 = 1,a_2=1.5,a_3=2,a_4=2.5,a_5=3$

Sums of these to each point....

$a_1=1, a_2=2.5, a_3=4.5, a_4=7, a_5=10$

It doesn't seem like it should be too tricky to figure out how to get a formula for a sum of the first N terms, since each term seems to just increase by 0.5 every team, I just haven't done this for a while and am a little rusty. Any pointers would be greatly appreciated!

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Do you know how to sum an Arithmetic Progression? – Rijul Saini Sep 5 '12 at 15:58
Got it! Thank you. Answer seems to be $n/2(a_1 + a_{n})$ – Hoser Sep 5 '12 at 16:02
@Hoser: correct, but it is better to write $n(a_1+a_n)/2$ so it is obvious that the $(a_1+a_n)$ is in the numerator. – Ross Millikan Sep 5 '12 at 16:08
Yeah I see what you mean. Thanks! – Hoser Sep 5 '12 at 16:19
The trick is to show that $a_i$ is an arithmetic progression. – Thomas Andrews Sep 5 '12 at 16:53