User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/existence

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/integrand

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/evaluation

User:GFauxPas/Sandbox/Zeta2/FourierSeries/

User:GFauxPas/Sandbox/Zeta2/Informal Proof

The proof proceeds by induction on $n$, the power of $x^n$.

Basis for the Induction
If $n=1$, then $x^n = x^1 = x$.

The result then follows from Limit at Infinity of Identity Function. This is the basis for the induction.

Induction Hypothesis
Fix $n-1 \in \N$ with $n \ge 2$.

Assume to-be-proved property holds for $n$.

This is our induction hypothesis.

Induction Step
This is our induction step:

''Insert reasoning. Whenever the induction hypothesis is used, write down explicitly that this is done.''

When desired, use the reference induction hypothesis.

We conclude to-be-proved property holds for $n+1$.

The result follows by the Principle of Mathematical Induction.