calcul-n-1-oo-1-n-2n-1-n-n-1-

Question Number 197349 by SANOGO last updated on 14/Sep/23

c a l c u l

\underset{n = 1}{\sum^{+ o o}} {(- 1)}^{n} \frac{2 n + 1}{n (n + 1)}

Answered by MM42 last updated on 14/Sep/23

\frac{2 n + 1}{n (n + 1)} = \frac{1}{n} + \frac{1}{n + 1}

s_{n} = - (\frac{1}{1} + \frac{1}{2}) + (\frac{1}{2} + \frac{1}{3}) - (\frac{1}{3} + \frac{1}{4}) - \dots

s_{n} = - 1 \pm \frac{1}{n + 1} \Rightarrow s = {l i m}_{n \to \infty} s_{n} = - 1

Commented by SANOGO last updated on 14/Sep/23

m e r c i

Commented by MathematicalUser2357 last updated on 16/Sep/23

r o n a l d o