I developed Math Fun Facts in 1994 as a warm-up activity for the calculus courses I taught as a graduate...

Continue reading...# infinite series

## Euler’s Product Formula

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...## Taylor-made Pi

After learning about the Taylor series for 1/(1+x) in calculus, you can find an interesting expression for Pi very easily. Start with...

Continue reading...## Tower of Powers

Consider an infinite “tower of powers” of x, defined by x^x^x^… = x^(x^(x^…)) Can we find a value of x...

Continue reading...## 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...

Continue reading...