sum from k=1 to infinity of (cos(10))^k

Lösung

k = 1 \sum \infty (cos (10))^{k}

konvergiert

Schritte zur Lösung

k = 1 \sum \infty (cos (10))^{k}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= k = 0 \sum \infty (cos (10))^{k} - (cos (10))^{0}

k = 0 \sum \infty (cos (10))^{k} =

konvergiert

= konvergiert - (cos (10))^{0}

= konvergiert

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{3}

n = 1 \sum \infty cos (\frac{16}{n})

n = 1 \sum \infty \frac{1}{n ^{4} + 2 n + 8}

n = 0 \sum \infty \frac{n}{n + 4}

n = 0 \sum \infty \frac{3}{n ( n + 2 )}