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The sum of the reciprocal of the triangular numbers up to $\frac1{t_n}$ is < 2
I am supposed to prove that $(1/1) + (1/3) + (1/6) + \dots + (1/t_n) < 2$.
The hint is that
$$
\frac2{n(n+1)} = 2\left(\frac1{n} - \frac1{n+1}\right)
$$
However, I was thinking that if you ...
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