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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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