What is the sum from n=0 to infinity of (1+7n)^{1/2} ?

The sum from n=0 to infinity of (1+7n)^{1/2} is diverges

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sum from n=0 to infinity of (1+7n)^{1/2}

n = 0 \sum \infty (1 + 7 n)^{\frac{1}{2}}

diverges

Solution steps

n = 0 \sum \infty (1 + 7 n)^{\frac{1}{2}}

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty \frac{1}{( n ) ^{2}}

n = 0 \sum \infty \frac{9}{5 ^{n}}

n = 1 \sum \infty (- \frac{1}{2})^{n + 3}

n = 1 \sum \infty \frac{2 n}{1 + n ^{2}}

n = 1 \sum \infty \frac{( 2 ) ^{n}}{n}

What is the sum from n=0 to infinity of (1+7n)^{1/2} ?
The sum from n=0 to infinity of (1+7n)^{1/2} is diverges