sum from n=0 to infinity of 4(1/10)^n

解答

n = 0 \sum \infty 4 (\frac{1}{10})^{n}

\frac{40}{9}

十进制

4.44444 \dots

求解步骤

n = 0 \sum \infty 4 (\frac{1}{10})^{n}

使用常数相乘法则:

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

= 4 \cdot n = 0 \sum \infty (\frac{1}{10})^{n}

使用几何级数审敛法:

\frac{10}{9}

= 4 \cdot \frac{10}{9}

化简

4 \cdot \frac{10}{9} : \frac{40}{9}

= \frac{40}{9}

t^{2} y^{^{'}} + t y = 7

\int \frac{x ^{2}}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

d er i v a t i v e f (x) = \frac{27}{5 e ^{2}} - \frac{3}{2}

\frac{d}{d x} (x + 1 (16 + 8 x + 9 x^{2}))

x y^{^{'}} + y = y^{2}, y (1) = - 7