Heys I'm having a few problems understanding a few worded questions and wonder if anyone may be able to help me.

1. Suppose that an infinite series has the property that, given any positive number, all but

finitely many terms of the series are positive and less than this number. Does it follow that

this series converges?

2. Can one ever obtain a convergent infinite series by interspersing the terms of two divergent

series?

3. Given any positive number, all but infinitely many partial sums of a certain infinite series aregreater than this number. Does it then follow that this series diverges?

4. Can one determine whether a given infinite series converges or diverges merely by computing

a suciently large number of partial sums?

5. Can one determine the sum|accurate to a given fixed number of decimal places|of a

convergent geometric series merely by computing a suciently large number of partial sums?

Thanks in advance