Infinite series — the sum of infinitely many numbers, variables or functions that follow a certain rule — are bit players in the great drama of calculus. While derivatives and integrals rightly steal ...

Yesterday, I posted an article about a math video that showed how you can sum up an infinite series of numbers to get a result of, weirdly enough, -1/12. A lot of stuff happened after I posted it.

We know the sum is less than 80 (for any digit except 0), but with the 9's removed the actual sum is approximately 22.92067. Series are great fun and they will make an appearance again when I ...

Also Erdminnelchen asked, if the harmonic series is infinite and 1 plus 1/2 plus 1/4 plus 1/8 and so in is finite, is there an infinite sum between those sums when is on the edge of being infinite ...

This series converges even when x = 1 and since we know that arctan(1) = π/4, we then get the infinite series representation That's pretty cool. Unfortunately, it's not that efficient.

For example: 1/2 + 1/4 + 1/8 + 1/16 + . . . That series will go on to forever, and you understand how it will go. You also understand what the sum of all those infinite terms will be.

To get over this difficulty, we may use a generalization of the process of finding the sum of an infinite series, such as that due to Cesaro. It may be recalled that Hardy and Rogosinski, ...