```Date: Feb 16, 2013 1:42 AM
Author: David Bernier
Subject: Bernoulli numbers and sqrt(1)+sqrt(2)+sqrt(3) + ... sqrt(1000)

The Bernoulli numbers can be used to compute for example1^10 + 2^10 + ... + 1000^10 .Jakob Bernoulli wrote around 1700-1713 that he had computedthe sum of the 10th powers of the integers 1 through 1000,with the result:91409924241424243424241924242500in less than "one half of a quarter hour" ...Suppose we change the exponent from 10 to 1/2, so the sumis then:sqrt(1) + sqrt(2) + ... sqrt(1000).Or, more generally,sqrt(1) + sqrt(2) + ... sqrt(N)  , N some largish positiveinteger.Can Bernoulli numbers or some generalization be usedto compute that efficiently and accurately?My first thought would be that the Euler-MacLaurinsummation method might be applicable.Above, if k^a is the k'th term, a = 1/2 .There's also a= -1 that leads to partial sums ofthe harmonic series.David Bernier-- dracut:/# lvm vgcfgrestoreFile descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh   Please specify a *single* volume group to restore.
```