Here is an amazing formula due to Euler:SUMn=1 to infinity n-s = PRODp prime (1 – p-s)-1 .What’s interesting about this formula is that it...

Continue reading...# infinite series

## Thinned-Out Harmonic Series

You’re probably already aware that the harmonic series, which is the sum of the reciprocals of all natural numbers, diverges. In...

Continue reading...## Sums of Reciprocal Powers

You have seen that the harmonic series diverges. What about the sum of reciprocal squares? In fact, they converge, and to something...

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