Since

< for all n: < 1Which means that the series converges, although I know of no tests that actually find this number.

And why isn't the latex '<' not working?

]]>I meant such that (x+1) = sin( (x) )]]>

ii. It stands to reason that, although the numbers will get so small as to be essentially 0, there will always be some teeny tiny insignificant bit more to add. I wouldn't know how to find out, though.

iii. Sure there is: ƒ(x) = sin(x-1)]]>

a_0 = 1

and for each successive term;

a_n+1 = sin(a_n)

i. The infinite limit of the sequence a_n is 0, right?

ii. Does this infinite series have a finite sum? If so, what is it?

iii. Is there any explicit function (x) such that (x+1) = sin( (x) )?

-thanks

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