Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

sum Series

sum Series
1/(log 2) + 1/(log 2)(log 3) + 1/(log 2)(log 3)(log 4) + ...

1/(sin²1)² + 1/(sin²1+sin²2)² + 1/(sin²1+sin²2+sin²3)² + 1/(sin²1+sin²2+sin²3+sin²4)² + .

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: sum Series

I found where you took these problems from: http://www.contestcen.com/conv.htm

The instructions say that we only need to determine whether the series converge or diverge; it doesn’t say that we have to evaluate the sum if the series is convergent. Also, the instructions say that the log is natural logarithm. If that’s the case, then 1⁄(log(3)) <  1 and the first one becomes a piece of cake.

So the sequence of partial sums is increasing and bounded above – hence the series is convergent! If it’s not required to find what it converges to, then that’s it. That’s the first problem solved.

Second problem … umm …

BTW, I think this is the last of Tony’s threads in this forum that has (prior to this post) not had any replies. If there are any more unanswered threads by Tony, I’d like to find them.

Last edited by JaneFairfax (2007-12-19 23:34:17)