if-z-e-z-1-n-0-B-n-z-n-n-1-calculate-B-0-B-1-B-2-B-3-B-4-2-prove-that-z-1-e-z-1-1-2-is-a-odd-function-conclude-that-B-2n-1-0-for-n-1-

Question Number 67519 by mathmax by abdo last updated on 28/Aug/19

i f \frac{z}{e^{z} - 1} = \sum_{n = 0}^{\infty} B_{n} \frac{z^{n}}{n!}

1) c a l c u l a t e B_{0}, B_{1}, B_{2}, B_{3}, B_{4}

2) p r o v e t h a t z \to \frac{1}{e^{z} - 1} + \frac{1}{2} i s a o d d f u n c t i o n c o n c l u d e t h a t

B_{2 n + 1} = 0 f o r n ⩾ 1