# Silkos advanced mathematics problems question 3ii

If you don't know the question, you can find it online. The whole book is free to download. It involves sequences and proofs.

In part ii, we're given a few equations and it says that we should find and prove a general rule wherein the equations below are special cases.

However, the answers bit doesn't tell me anything about how I get to the equation. It tells me how to prove it, but I have no clue on how to get to the equation in the first place. Could anyone give some insight? I am completely lost.

### This is just a matter of

This is just a matter of spotting a pattern which you get better at the more you do maths. On the left hand side, you can spot that the sum goes from a square number + 1 i.e. $m^2+1$ to the next square number i.e. $(m+1)^2$. The right hand side is easier to spot; it's just the sum of $m^3$ and $(m+1)^3$.

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