sum from n=1 to infinity of 1*(1/5)^n

解

n = 1 \sum \infty 1 \cdot (\frac{1}{5})^{n}

\frac{1}{4}

十進法表記

0.25

解答ステップ

n = 1 \sum \infty 1 \cdot (\frac{1}{5})^{n}

簡素化

= n = 1 \sum \infty (\frac{1}{5})^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty (\frac{1}{5})^{n} - (\frac{1}{5})^{0}

n = 0 \sum \infty (\frac{1}{5})^{n} = \frac{5}{4}

= \frac{5}{4} - (\frac{1}{5})^{0}

簡素化

\frac{5}{4} - (\frac{1}{5})^{0} : \frac{1}{4}

= \frac{1}{4}