What is the sum from n=1 to infinity of (8^n)/(7^n) ?

The sum from n=1 to infinity of (8^n)/(7^n) is diverges

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sum from n=1 to infinity of (8^n)/(7^n)

n = 1 \sum \infty \frac{8 ^{n}}{7 ^{n}}

diverges

Solution steps

n = 1 \sum \infty \frac{8 ^{n}}{7 ^{n}}

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= n = 1 \sum \infty (\frac{8}{7})^{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{8}{7})^{n} - (\frac{8}{7})^{0}

n = 0 \sum \infty (\frac{8}{7})^{n} =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

n = 6 \sum \infty ln (1 + \frac{1}{n})

n = 0 \sum \infty \frac{2}{1 - n ^{2}}

n = 1 \sum \infty 5 \cdot 0. 2^{n - 1}

k = 1 \sum \infty \frac{2}{k ( k + 2 )}

n = 1 \sum \infty (0.6)^{n - 1}

What is the sum from n=1 to infinity of (8^n)/(7^n) ?
The sum from n=1 to infinity of (8^n)/(7^n) is diverges