sum from n=1 to infinity of 4/(n^2+5n+6)

解答

n = 1 \sum \infty \frac{4}{n ^{2} + 5 n + 6}

\frac{4}{3}

十进制

1.33333 \dots

求解步骤

n = 1 \sum \infty \frac{4}{n ^{2} + 5 n + 6}

使用常数相乘法则:

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

= 4 \cdot n = 1 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

使用裂项级数审敛法:

\frac{1}{3}

= 4 \cdot \frac{1}{3}

化简

4 \cdot \frac{1}{3} : \frac{4}{3}

= \frac{4}{3}

\int \frac{sin ( \frac{9}{x} )}{x ^{2}} d x

\frac{\partial}{\partial x} (x^{2} - 10 x + y^{2} + 8)

in v erse l a pl a ce \frac{1}{( s ^{3} + 4 s )}

l a pl a ce t r an s f or m 10 (t - 1)

(2 x - 5 y + 2) d x + (1 - 6 y - 5 x) d y = 0