What is the sum from n=0 to infinity of 2/(sqrt(n)) ?

The sum from n=0 to infinity of 2/(sqrt(n)) is diverges

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sum from n=0 to infinity of 2/(sqrt(n))

n = 0 \sum \infty \frac{2}{n}

diverges

Solution steps

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

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{n}

Apply p-Series Test:

diverges

= 2 diverges

= diverges

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

n = 1 \sum \infty 2 + e^{- n}

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

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

n = 0 \sum \infty π e^{- n}

What is the sum from n=0 to infinity of 2/(sqrt(n)) ?
The sum from n=0 to infinity of 2/(sqrt(n)) is diverges