Let |z_n+1/z_n| ‰¤ q < 1, so that the series z₁+ z₂+ · · · converges by the ratio test. Show that the remainder R_n= z_n+1+ z_n+2+ · · · satisfies the inequality |R_n| ‰¤ |z_n+1|/(1 - q). Using this, find how many terms suffice for computing the sum s of the series

with an error not exceeding 0.05 and compute s to this accuracy.

Transcribed Image Text:

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