Question

Does this sum converge: show steps

Answer 1

Yes

Explanation:

`\sum_(n=1)^(\infty) e^(-√(n) ) \\\sum_(n=1)^(\infty) ((1)/(e))^(√(n) )`

If we say u = √n, then:

`\sum_(u=1)^(\infty) ((1)/(e))^(u)`

This is a geometric series. Since |1/e| < 1, the series converges.