Submitted by Heirio on Sun, 08/27/2017 - 21:06
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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 $(m+1)^3$.