How do you prove that infinite sequences converge? For example how did someone prove that 1 + 1/4 + 1/9 + 1/16 + 1/25 ..... conv

Question

3 years ago

9

How do you prove that infinite sequences converge? For example how did someone prove that 1 + 1/4 + 1/9 + 1/16 + 1/25 ..... conv

erges to π^2/6. Can someone explain how people do this, and the process to discovering whether or not infinite sequences diverge or converge? An answer fully explaining the process, that is also fairly clear will receive a brainiliest.

Mathematics

1 answer:

dem82 [27] · Answer 1 · 2022-05-22T14:07:18+03:00

dem82 [27]3 years ago

4 0

Answer:Prove that for any nonzero natural

n

it is true that

Sn=1+1/4+1/9+1/16+1/25+1/2<2

I'm sort of at a loss here. I'm not sure if there exists some formula or method to sum this kind of series, since there is a variable ratio…