What is the sum from n=1 to infinity of (1000)/(5^n) ?

The sum from n=1 to infinity of (1000)/(5^n) is 250

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sum from n=1 to infinity of (1000)/(5^n)

n = 1 \sum \infty \frac{1000}{5 ^{n}}

250

Solution steps

n = 1 \sum \infty \frac{1000}{5 ^{n}}

Apply the constant multiplication rule:

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

= 1000 \cdot 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}

= 1000 (n = 0 \sum \infty \frac{1}{5 ^{n}} - \frac{1}{5 ^{0}})

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

= 1000 (\frac{5}{4} - \frac{1}{5 ^{0}})

Simplify

1000 (\frac{5}{4} - \frac{1}{5 ^{0}}) : 250

= 250

l a pl a ce t r an s f or m 5 + 4 e^{- 2 t}

\int (2 x) d x

\int x + y d x

\int y cos (\frac{y ^{2}}{x ^{2}}) d y

a re a x^{2} - 43, 5 - 2 x

What is the sum from n=1 to infinity of (1000)/(5^n) ?
The sum from n=1 to infinity of (1000)/(5^n) is 250