sum from n=1 to infinity of (5^n)/(n^2)

Lösung

n = 1 \sum \infty \frac{5 ^{n}}{n ^{2}}

divergiert

Schritte zur Lösung

n = 1 \sum \infty \frac{5 ^{n}}{n ^{2}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{n ^{2}}}{\frac{5 ^{n + 1}}{( n + 1 ) ^{2}}} - 1)) = - \infty

L < 1,

aufgrund des Raabe Tests

= divergiert

n = 4 \sum \infty \frac{3}{n ^{2} - n}

m = 2 \sum \infty \frac{2}{3 ^{m}}

n = 0 \sum \infty \frac{1}{( 1 - 3 n ) ^{3}}

n = 1 \sum \infty (\frac{e}{π})^{n + 1}

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