1n n12 nSolution use alternating series test the sqrtn12sqrt

(-1)n n/1+2 n

Solution

use alternating series test. the sqrt(n)/(1+2*sqrt(n)) must go to 0 for the series to converge. but as n goes to infinity this term approaches sqrt(n)/2*sqrt(n) for big values of n and this reduces to 1/2. thus for really big values of n this series alternates between -1/2 and +1/2 so the sum does not converge to anything. therefore the series is divergent