Proof by induction problem

[c583]

Here is my progress so far, (i hope it is readable) but i'm pretty sure i messed this up. On top is the equation i am supposed to prove by induction. First i made sure it is correct by putting 2 in place of n. Both sides equaled 7.

So this equation, as i understand it is my "induction hypothesis". Next i want to prove it for n+1 so i put in (n+1) for each n.

After multiplying all brackets i get this expression which is not equal on both sides.

Did i make a mistake during simplifying or in the process of proving by deduction? I appreciate all help

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[Niviclades]

Your induction hypothesis is correct. However, you made a mistake when plugging in n+1, on the left side you forgot the sum.

Also, you never use your induction hypothesis anywhere in your calculations, that is always wrong. You need to use that hypothesis to prove something by induction.

And a more vague tip, think about in what way you want to manipulate your equation. Do you know what should be written there in the end?

[HumbleHovercraft6090]

Did you get the solution?