Add new comment
Some practical tips to help you when you need it most!
-
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
A basic introduction to the most powerful tools in science and enginnering.
As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.
How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.
Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.
Find out why the formula we use to work out conditional probabilities is true!
I saw a demonstration of this sum recently. It went like this:
S=1-1+1-1+...
=1-(1-1+1-...)
the periods indicating a continuation to infinity, it is assumed that:
S=1-S
2S=1
S=1/2
Then again, the alternating harmonic series converges to ln2 but by rearranging the terms in the equation, it also converges to (ln2)/2 and (ln2)/4 and so forth. The problem in your reasoning is that you take a partial sum as reference. I know that it's counter-intuitive just like 0.00000...1= 0 but the reason it gives that result is only because the sum is infinite. The moment it becomes finite, these results all go wrong.