infinite series

About Math Fun Facts

Posted on July 11, 2019 by Francis Su

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

Posted on June 29, 2019 by Samuel Nunoo

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...

Posted on June 29, 2019 by Samuel Nunoo

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

Posted on June 28, 2019 by Samuel Nunoo

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

Posted on June 27, 2019 by Samuel Nunoo

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

Posted on June 26, 2019 by Samuel Nunoo

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