Hello! I got one issue with proving divergence of series. I start covering this part of mathematics and don't understand how to prove it. Here is the issue:(adsbygoogle = window.adsbygoogle || []).push({});

I got one harmonic series:

[tex]\sum_{n=1}^{\infty}{\frac{1}{n}}=1 + \frac{1}{2} + \frac{1}{3} +...[/tex]

We need to show that the series of partial sums (separate sums) is not bounded.

X_{n}=1 + 1/2 +1/3 +...+ 1/n

As I can see:

X_{2}=1 + 1/2 = X_{1}+ 1/2

but what I can't understand is:

X_{4}=X_{22}=1 + 1/2 + 1/3 + 1/4 > 1 + 1/2 + 2*1/4 = 1 + 2/2

and

X_{2k}>1 + k/2 where k>1

Can you please give me a short explanation that would help me understand?

Thanks in advance.

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# [prove] Divergence of series

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