How to show that, $\sum_{n=1}^N 1/n$ $\le$ 1 + logN, for N$\ge$5
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Look up the approximation for the Harmonic series – Henry Lee Jul 04 '20 at 16:07
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Isn't it true for all $N?$ – zhw. Jul 04 '20 at 16:28
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hint
For any $ n\ge 2$, and any $ t\in [n-1,n] $,
$$\frac{1}{n}\le \frac 1t \;\implies$$
$$\int_{n-1}^n\frac {dt}{n}\le \int_{n-1}^n\frac{dt}{t} \;\implies$$ $$\frac{1}{n}\le \ln(n)-\ln(n-1)$$
hamam_Abdallah
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