Sequences & series

1. Find a formula general for the
general term for the following sequences:

Determine if they are convergent
or divergent. If the sequence is convergent find its limit.

2.Let: a1=2 ��.

a.Reasoning by induction show that
0<an=<2

b.show by induction for what n the
sequence is decreasing.

c.Suppose that an is convergent
and find its limit

3.Suppose that the partial sum of
the series�. is given by �� Find a)b)c)

4.Determine whether series
coverges or not. If yes find its sum.

5.Using the integral test, find
for what values of p the series is convergent.

6.Using lnx<â??x if x>0,
test the series for convergance.

7.Using convergence tests (limit
comparison test, ratio test, root test) test whether the series is convergent
or divergent.

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