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I've just started to learn some mathematical induction and it's proving quite tricky. Hopefully someone could help me out a little with my questions!

I don't know how to format question on this forum but I'll try my best to accurately represent it:

n

\(\displaystyle sigma\) i * 2^i = (n-1) * (2^n+1) + 2

i=1

Now, I know that I have to prove for the base case, which I take it to be 0. If I do so, it holds true however I don't know what the meaning of i=1 under the sigma represents. Does that mean the base case must equal 1? If so it doesn't work out I think.

If anyone could help me figure out this one problem, that'd be awesome!

Thank you!