What is the sum from n=0 to infinity of (1000)/n ?

The sum from n=0 to infinity of (1000)/n is diverges

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sum from n=0 to infinity of (1000)/n

n = 0 \sum \infty \frac{1000}{n}

diverges

Solution steps

n = 1 \sum \infty \frac{1000}{n}

Apply the constant multiplication rule:

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

= 1000 \cdot n = 1 \sum \infty \frac{1}{n}

Apply Cauchy's Convergence Condition:

diverges

= 1000 diverges

= diverges

What is the sum from n=0 to infinity of (1000)/n ?
The sum from n=0 to infinity of (1000)/n is diverges