3. Using a simulation of three decimal digit arithmetic on a com- puter, find the sum of the "infinite" series: i=1 (a) Starting from 1 keep adding terms until you encounter a term 1/n, such that it does not affect the sum and print out the value of n and the sum. (b) Starting from 1/(n–1), sum the series in backward direction. (c) Starting from 1/(10n), sum the series in backward direction. (d) Repeat the steps (a), (b) and (c) for five decimal digit arith- metic. (e) Try to estimate the value of the sum if step (a) is carried out on a computer using 48-bit or 50-bit arithmetic. (Warning: do not try to verify this result experimentally.)

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