Find the first three partial sum and the nth partial sum of the sequence given by: An= sqrt n - sqrt n+1. As n approaches infinity, what is Sn approaching? (in other words, what happens to Sn as n gets larger?). Please show all work. Thanks! Solution S1 = 1-sqrt2 S2 = 1- sqrt (3) [sqrtn+1 and sqrt from the next cancels] S3 = 1 -sqrt(4) = 1-2 = -1 nth ppartial sum = 1 -sqrtn+1.

1. Find the first three partial sum and the nth partial sum of the sequence given by: An= sqrt n - sqrt
n+1. As n approaches infinity, what is Sn approaching? (in other words, what happens to Sn as n
gets larger?). Please show all work. Thanks!
Solution
S1 = 1-sqrt2
S2 = 1- sqrt (3) [sqrtn+1 and sqrt from the next cancels]
S3 = 1 -sqrt(4) = 1-2 = -1
nth ppartial sum = 1 -sqrtn+1