What is the sum from n=0 to infinity of 4/(sqrt(n)) ?

The sum from n=0 to infinity of 4/(sqrt(n)) is diverges

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sum from n=0 to infinity of 4/(sqrt(n))

n = 0 \sum \infty \frac{4}{n}

diverges

Solution steps

n = 1 \sum \infty \frac{4}{n}

Apply the constant multiplication rule:

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

= 4 \cdot n = 1 \sum \infty \frac{1}{n}

Apply p-Series Test:

diverges

= 4 diverges

= diverges

n = 1 \sum \infty \frac{2}{n ^{0.45}}

n = 0 \sum \infty \frac{n}{10 n ^{6} + 1}

n = 0 \sum \infty \frac{3}{2 ^{n - 1}}

n = 1 \sum \infty \frac{5 ^{n}}{8}

n = 0 \sum \infty \frac{n}{49 + n ^{2}}

What is the sum from n=0 to infinity of 4/(sqrt(n)) ?
The sum from n=0 to infinity of 4/(sqrt(n)) is diverges