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

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

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sum from n=0 to infinity of 2/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 Cauchy's Convergence Condition:

diverges

= 2 diverges

= diverges

n = 1 \sum \infty \frac{6 ^{n}}{n !}

n = 1 \sum \infty \frac{n ^{n}}{3 ^{n}}

n = 1 \sum \infty \frac{1}{6 ^{n} - 5}

n = 9 \sum \infty \frac{n !}{n ^{n}}

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

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