What is the sum from n=0 to infinity of 5/(sqrt(n)) ?

The sum from n=0 to infinity of 5/(sqrt(n)) is diverges

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sum from n=0 to infinity of 5/(sqrt(n))

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n}

Apply p-Series Test:

diverges

= 5 diverges

= diverges

n = 0 \sum \infty ∣ n ∣

n = 0 \sum \infty (\frac{7}{5})^{n}

n = 0 \sum \infty \frac{sin ( \frac{1}{n} )}{n}

n = 0 \sum \infty 3 + 15 + 75 + 375

n = 1 \sum \infty \frac{5}{2 ^{n - 2}}

What is the sum from n=0 to infinity of 5/(sqrt(n)) ?
The sum from n=0 to infinity of 5/(sqrt(n)) is diverges