SOMEONE ASKED ๐
How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
HERE THE ANSWERS ๐

Since these are alternating series, we only need to find when the absolute value of the nth term is less than the given error.
(The error after taking n terms in an alternating series is bounded above in absolute value by the following term.)
1) We need 1/n^2 < 0.004
==> n^2 > 1/0.004 = 250
==> n > sqrt(250), which is just under 16.
So, if we use 15 terms, then we will have the desired accuracy.
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2) We need 7/n^4 < 0.0005
==> n^2 > 14000
==> n > sqrt(14000), which is just over 118.
So, if we use 118 terms, then we will have the desired accuracy.
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I hope this helps!
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