Pure Mathematics
Statistics

Worked Example 4

(i)

By considering [latex]\text{f}\left( r \right)-\text{f}\left( r+1 \right)[/latex], where [latex]\text{f}\left( r \right)=\frac{1}{r}[/latex], find the sum to [latex]2n[/latex] terms of the series [latex]\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+…[/latex]

(ii)

Show that the sum to [latex]2n[/latex] terms of the series [latex]\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}}+\frac{1}{{{5}^{2}}}+…[/latex] is less than [latex]1[/latex].

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