Comments on: Mathematical induction with an inequality

By: Umar Farouk

Umar Farouk — Tue, 30 Apr 2019 19:17:56 +0000

yes, this does help as i was lost on the same step.

By: UCT MAM1000W lecture notes subject links – Mathemafrica

UCT MAM1000W lecture notes subject links – Mathemafrica — Thu, 15 Mar 2018 10:29:22 +0000

[…] Mathematical induction with an inequalityProof by induction winning explanation […]

By: Mufhatutshedzwa Nemakhavhani

Mufhatutshedzwa Nemakhavhani — Wed, 19 Apr 2017 23:38:20 +0000

Thank you Dr Shock for such a wonderful explanation.

By: Jonathan Shock

Jonathan Shock — Fri, 11 Mar 2016 09:33:57 +0000

If we have (1+a)^b, we can write this is (a(1+1/a))^b, and we know that if we have (pq)^r, this is p^rq^r, so therefore (a(1+1/a))^b=a^b(1+1/a)^b. In this case a is n and b is 3. Does that help?

By: Greg

Greg — Fri, 11 Mar 2016 09:26:54 +0000

“ok, now we have to do some inspection. We want to get the right hand side somehow to look like (n+1)^3 but at the moment, we just have n^3. In fact one can write: (n+1)^3 = n^3(1+1/n)^3”

I really don’t understand this step at all. Please explain why and how you went from (n+1)^3 to (n+1)^3 = n^3(1+1/n)^3

Thank you kindly.

By: Jonathan Shock

Jonathan Shock — Thu, 10 Mar 2016 16:13:44 +0000

In this case you have to be a bit careful as it is only true for n>=10, so you can say “Suppose for an arbitrary natural number>=10, that…”

By: Kabelo

Kabelo — Thu, 10 Mar 2016 08:02:06 +0000

Can we phrase for exam purposes, the inductive hypothesis: as “Suppose for an arbitrary natural number n, that 2^n > n^3…”?

By: Tshepiso

Tshepiso — Wed, 09 Mar 2016 22:49:00 +0000

Thank you very much Dr Shock!

By: Josh

Josh — Wed, 09 Mar 2016 18:57:08 +0000

Thank you!

By: Shai

Shai — Wed, 09 Mar 2016 16:50:23 +0000

Thanks for clarifying, Doc Shock!