Question

is the series sum[n=1,infinity](1-sqrt(1-(1/n))) convergent or divergent?

Answer 1

Would you be willing to try the integral test?

Answer 2

@melaniebrown, you're given a positive and decreasing series, do you think you'd be able to integrate
\[\int_1^\infty \left(1-\sqrt{1-\frac{1}{x}}\right)~dx ~~?\]

Answer 3

Alternatively, you can try comparing to a known divergent/convergent series and see what you get. I have a feeling this series diverges, so I would try comparing to \(\sum\dfrac{1}{\sqrt n}\).