What is the sum from n=3 to infinity of 5^n ?

The sum from n=3 to infinity of 5^n is diverges

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sum from n=3 to infinity of 5^n

n = 3 \sum \infty 5^{n}

diverges

Solution steps

n = 3 \sum \infty 5^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty 5^{n} - 5^{0} - 5^{1} - 5^{2}

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

What is the sum from n=3 to infinity of 5^n ?
The sum from n=3 to infinity of 5^n is diverges