mathematical induction problem

i cannot figure out how to know that [k-1]^2 has to be ''picked-out''

i have no idea how to do this type of question also.

sorry for my bad hand-writing

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- Jan 12th 2008, 02:14 AMafeasfaerw23231233mathematical induction problem
mathematical induction problem

i cannot figure out how to know that [k-1]^2 has to be ''picked-out''

i have no idea how to do this type of question also.

sorry for my bad hand-writing - Jan 12th 2008, 08:22 PMmr fantastic
You

*do*understand that you're working towards the final line being > (k + 1)^2? So the k^2 gets replaced with (k - 1)^2 + 2k -1 because (k - 1)^2 is bigger than 2 for k > 4 and so you can write the second last line, which will give you the final line ......

It's a trick that once seen you*memorise*and then learn to*generalise*- as in the second problem, where you need to work towards the final line being > (k + 1)^3.