Bernoulli numbers

Compute the first few Bernoulli numbers.

> seq(bernoulli(i),i=0..16);

[Maple Math]

Now time the computation of the one thousandth Bernoulli number.

> st := time(): b1000 := bernoulli(1000): t1 := time()-st;

[Maple Math]

Now use Euler's formula for Zeta(1000) .

> st := time():

> Digits := 2000:

> zeta_1000 := add(1./i^1000,i=1..100):

> B := zeta_1000*2*1000!/evalf((2*Pi)^1000):

> B := -(-1)^irem(1000/2,2)*B:

> Digits := Digits-12:

> B := evalf(B):

> B := convert(B,rational):

> t2 := time()-st;

[Maple Math]

Check the answer.

> zero_4 := b1000-B;

[Maple Math]

It was more than 10 times faster to use Euler's formula than it was to use the Maple procedure bernoulli(1000), but the procedure did compute all the even indexed Bernoulli numbers up to 1000.