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Tuesday, March 23, 2010

Proof that harmonic series diverges

Let $H_n=\sum_{k=1}^n{\frac{1}{k}}$
We investigate $H_{2^k}$
&\gt \frac{1}{1}+\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})\\
&\gt \frac{1}{1}+\frac{1}{2}+\frac{1}{2}\\

&\gt \frac{1}{1}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\\
By induction it can be shown that
Since we can make $k(\frac{1}{2})$ as large as we want by choosing a value for $k$ this implies that we can also make $H_{2^k}$ as large as want, i.e. $H$ diverges.

Started on MT365-TMA01/CMA41. Started on question 1 and got lost in the mechanics of GraphPlot and it's options. Learned some Mathematica again. I have to increase my efforts on MT365. Yellow Alert.

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