sum from n=1 to infinity of (3n)/(n!)

解答

n = 1 \sum \infty \frac{3 n}{n !}

收敛

求解步骤

n = 1 \sum \infty \frac{3 n}{n !}

使用常数相乘法则:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 3 \cdot n = 1 \sum \infty \frac{n}{n !}

使用级数比值审敛法:

收敛

= 3 收敛

= 收敛

\int csc^{3} (x) \cdot sec (x) d x

\int (x^{2} + a x - 3)^{2} d x

\int_{0}^{1} 2 x^{2} - 1 d x

\frac{d ^{2}}{d x ^{2}} ((x + 1) e^{x})

n = 1 \sum \infty sin (πn)