What is the sum from n=1 to infinity of 7/(e^n) ?

The sum from n=1 to infinity of 7/(e^n) is 7(e/(e-1)-1)

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

n = 1 \sum \infty \frac{7}{e ^{n}}

7 (\frac{e}{e - 1} - 1)

Solution steps

n = 1 \sum \infty \frac{7}{e ^{n}}

Apply the constant multiplication rule:

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

= 7 \cdot n = 1 \sum \infty \frac{1}{e ^{n}}

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

= 7 (n = 0 \sum \infty \frac{1}{e ^{n}} - \frac{1}{e ^{0}})

n = 0 \sum \infty \frac{1}{e ^{n}} = \frac{e}{e - 1}

= 7 (\frac{e}{e - 1} - \frac{1}{e ^{0}})

Simplify

= 7 (\frac{e}{e - 1} - 1)

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

n = 1 \sum \infty \frac{6 ^{n}}{n ^{3}}

n = 1 \sum \infty ln (2)

n = 1 \sum \infty sin (\frac{πn}{4})

n = 1 \sum \infty \frac{1}{6 ^{n} - 3}

What is the sum from n=1 to infinity of 7/(e^n) ?
The sum from n=1 to infinity of 7/(e^n) is 7(e/(e-1)-1)