# Talk:Apéry's constant

Latest comment: 11 months ago by Nigel Galloway

### What does 158 terms mean?

I assume "Show the value of the first 158 terms" (a 158 item list) means "Show the value of the 158th. term" (a single calculated value).--Nigel Galloway (talk) 15:32, 24 February 2023 (UTC)

- These are all sums of infinite series. Rather than summing infinity values, only sum 1000, 158, or 20 respectively. The 158th term has no particular significance on its own, only as being part of (and the terminus of,) a summation. So "showing the value the first 158 terms" would perhaps be more accurately phrased "show the value obtained by summing the first 158 terms". --Thundergnat (talk) 16:35, 24 February 2023 (UTC)

- The task requires "Show the value of Apéry's constant calculated at least three different ways". I was always going to add Apéry's continued fraction, which isn't the sum of an infinite series. I think the task really wants to know how many iterations are required to produce the 101 digits quoted, or if this is more than 1000 how many digits can be found with 1000 iterations. As this is a new task adding the continued fraction to the requirements may be good as this is of historic interest mathematically.--Nigel Galloway (talk) 14:22, 17 March 2023 (UTC)