Find the sum of the series ∞∑k=4, ((1/√k) − (1/√(k+1))

Answer 1

note how this series begins...
(1/√4 - 1/√5) + (1/√5 - 1/√6) + ...
When all the adjacent terms collapse, you are left with
1/√4 - 1/√∞ = 1/2