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## Homework Statement

Problem # 30 in Ch1 Section 16 in Mary L. Boas' Math Methods in the Physical Sciences

It is clear that you (or your computer) can’t find the sum of an infinite series

just by adding up the terms one by one. For example, to get [tex]\zeta (1.1)=\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ 1.1 } } } [/tex] (see Problem 15.22) with error < 0.005 takes about [tex]10^{33}[/tex] terms.

To see a simple alternative (for a series of positive decreasing terms) look at

Figures 6.1 and 6.2. Show that when you have summed N terms, the sum RN

of the rest of the series is between [tex]{ I }_{ N }=\int _{ N }^{ \infty }{ { a }_{ n } } dn\quad and\quad { I }_{ N+1 }=\int _{ N+1 }^{ \infty }{ { a }_{ n } } dn[/tex]

## Homework Equations

They are above.

## The Attempt at a Solution

I am not sure how I am supposed to integrate an [tex] a_{n} [/tex] since it contains n!.

Thanks,

Chris Maness