Find the number of terms necessary to approximate the sum of the series with an error of less than 0.001 sigma on top infinity when n=1 [(1/n^2)].
Added by Mario C.
Step 1
The error bound is given by the integral from n to infinity of 1/x^2 dx. This simplifies to -1/x evaluated from n to infinity, which equals 1/n. Since we want the error to be less than 0.001, we have 1/n < 0.001. Therefore, n > 1/0.001 = 1000. ** Show more…
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