I've been struggling with learning mathematical induction in the past couple of days and I think I may have found out why but I still can't solve the problem due to a possible deficiency in foundational algebraic skills.

I'm not able to post an image as my account is too new but my textbook solution labels,

"replace 5+9+13+...+(4k+1) with k(2k+3).

It is this step that I always get stuck and I can't seem to see how I can replace the value with what they state in the example.

An explanation or some insight would be extremely helpful, thanks.


Its just sum if AP which is $$\frac{k}{2}(10+(4k-1)4)=2k^2+3k=k(2k+3)$$

  • 1
    $\begingroup$ Aha! Thank you, this really helps. $\endgroup$ – user318228 Feb 27 '16 at 12:58
  • $\begingroup$ Welcome :).... ... $\endgroup$ – Archis Welankar Feb 27 '16 at 13:20

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