sum from n=1 to infinity of (6n!)/(n^n)

解答

n = 1 \sum \infty \frac{6 n !}{n ^{n}}

收敛

求解步骤

n = 1 \sum \infty \frac{6 n !}{n ^{n}}

使用常数相乘法则:

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

= 6 \cdot n = 1 \sum \infty \frac{n !}{n ^{n}}

使用级数比值审敛法:

收敛

= 6 收敛

= 收敛

\frac{d}{d x} (\frac{x ^{2} - 5}{1 - 3 x ^{2}})

d er i v a t i v e 6 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (\frac{x ^{2} tan ( x ^{3} - x ^{2} )}{sec ( x )})

y^{^{''}} + 3 y^{^{'}} = 10 sin (t)

t an g e n t y = 5 x - 4 x, (1, 1)