Can you please correct your solution following Emy’s comment like you did with some other questions?
Some people don’t read the comments and it can leave them really confused.
Yes sorry I just haven’t had time yet.
Hi Emy, thanks for your comment. Yes my answer is wrong, thanks very much for pointing out the error.
I forgot that the series doesn’t converge when 0 < x <= 1, so for these values of x you can’t do the trick I did to rewrite the sum as x/(x-1) so this formula is not valid when x <= 1.
Looking at the sum it’s possible to see that its values are all infinite when x <= 1. So it makes sense to say that the inequality is true when x <= 1, and this would mean that the answer is 0 < x <= sqrt(2)
not 0< x < sqrt(2) ?
Yes you’re right, thanks for pointing that out. The expression x < √2 as written in the answer, is correct: not x ≤ √2 as written in the comment above.
I’m afraid I don’t know what happened to Emy’s original comment either. WordPress glitch…
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