# Simplify n(n+1)/2 + n+1

I cant seem to figure out how to simplify this!!!!

n(n+1)/2 + n+1

which they were able to get (n+1)(n+2)/2 by simplifying that

and this

n(n+1)(2n+6)/6 + (n+1)^2

and they were able to get (n+1)(n+1+1)(2(n+1)+1)/6 out of this one.

Any help is greatly appreciated.

Try this: surely you know how to "expand" parenthesis, like this: a(b+c) ---> ab + ac.

So do this both from the given problem expression, and also from the answer. Like this:
Problem -----> xxx
And try to get the same "xxx" starting from both ends.

When you have that, you can walk *forward* the steps from the problem, and then *backward* the steps from the solution:

ok i did that but for the first one i get

(n^2 + n)/2 + n + 1

=

n^2 + n + n + 1/2

= n^4 + 1/2

but this does not equal (n+1)(n+2)/2

You have only expanded the parenthesis on the initial problem... but have not expanded them yet on the solution. Try expanding (n+1)(n+2)/2.

And hey! Watch out, the /2 is dividing (n^2 + n), and only those two. Try again the first part.

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ooo I see I got it.. Thanks for the help!!