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#1 2007-04-10 07:29:58

virtualinsanity
Member
Registered: 2007-03-11
Posts: 38

Convergence problem (Calc)

If someone could explain how this problem is done, I would really appreciate it.

Let sigma starting at j=0 and ending at infinity of a_j be convergent, alternating series with |a_0|>=|a_1|>=|a_2|>=...

We'll call such a series a monotonic alternating series. Suppose that the series converges to s. Then |sigma starting at j=0 and ending at n of a_j -s| <= |a_n +1|. That is, the error is no more than the magnitude of the next term.

a) How close can we get to the sum of sigma starting at j=1 and ending at infinity of (-1)^j * (j+1)/(j!) with 6 terms (j=5)?

b) For this series, how many terms do we need to guarantee an answer within 0.001 of the actual sum?

Last edited by virtualinsanity (2007-04-10 07:30:33)

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