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人気のある微分積分 >

sum from k=1 to infinity of 1/(11^k)

解

k = 1 \sum \infty \frac{1}{1 1 ^{k}}

解

\frac{1}{10}

+1

十進法表記

0.1

解答ステップ

k = 1 \sum \infty \frac{1}{1 1 ^{k}}

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

= k = 0 \sum \infty \frac{1}{1 1 ^{k}} - \frac{1}{1 1 ^{0}}

k = 0 \sum \infty \frac{1}{1 1 ^{k}} = \frac{11}{10}

= \frac{11}{10} - \frac{1}{1 1 ^{0}}

簡素化

\frac{11}{10} - \frac{1}{1 1 ^{0}} : \frac{1}{10}

= \frac{1}{10}

人気の例

sum from n=1 to infinity of ((1-3)^n)/n

n = 1 \sum \infty \frac{( 1 - 3 ) ^{n}}{n}

sum from n=1 to infinity of (1/10)^{n-1}

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

sum from n=1 to infinity of 5(3/7)^n

n = 1 \sum \infty 5 (\frac{3}{7})^{n}

sum from n=1 to infinity of 1/24 (3/4)^n

n = 1 \sum \infty \frac{1}{24} (\frac{3}{4})^{n}

sum from n=0 to infinity of An*(-1)^n

n = 0 \sum \infty A n \cdot (- 1)^{n}