sum from n=0 to infinity of 6/(5^n)

解答

n = 0 \sum \infty \frac{6}{5 ^{n}}

\frac{15}{2}

十进制

7.5

求解步骤

n = 0 \sum \infty \frac{6}{5 ^{n}}

使用常数相乘法则:

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

= 6 \cdot n = 0 \sum \infty \frac{1}{5 ^{n}}

使用几何级数审敛法:

\frac{5}{4}

= 6 \cdot \frac{5}{4}

化简

6 \cdot \frac{5}{4} : \frac{15}{2}

= \frac{15}{2}

\int 2 sec (2 x) tan (2 x) d x

y^{^{'}} + (\frac{1}{x}) y = 8 x^{2}

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

t a y l or \frac{1}{1 + x ^{- 1}}

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 6, y^{^{'}} (0) = - 9