• # Question: What is the hardest sum you ever solved?

• Keywords:
Asked by daws52wye on 19 Oct 2022.
• Orla McManamly answered on 19 Oct 2022:

I always find it hard to know how much money I need to set aside today to have enough for when I’m older and no longer of working age. This is known as planning for retirement and it’s a hard sum because I need to think about what I want to do when I’m older and how much I will need for that, what I might own – e.g. a house – and how much it costs to run that and then how much the prices of things will change while I’m ageing. I also need to think about my health and how long I am likely to be able to work for. A lot to consider, and a hard sum to solve…..I’m still working on it!

• Harold Berjamin answered on 20 Oct 2022:

Sums don’t get solved: they get evaluated / computed. I don’t come much across sums, to be honest. When things look too hard, I evaluate the result numerically on a computer.

• Maja Popovic answered on 20 Oct 2022:

I don’t remember one single sum, it has been a while (I don’t use much sums nowadays), but the hardest ones were the infinite ones (summing infinitely many numbers) where you first have to figure out if the sum is infinity or something else, and then if not infinity, what exactly.

for example, sum of all whole numbers starting from 1 (1+2+3+4+….+infinity) is definitely infinity

for sum of all fractions (1/1 + 1/2 + 1/3 + 1/4 + … +1/infinity) it is not obvious, but it is again infinity

but, if you alternate the sign of the fractions (1/1 – 1/2 + 1/3 – 1/4…) then it’s not infinity!