Simplify the expression?: #1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))#
Simplify the expression:
#1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))#
Simplify the expression:
1 Answer
Mar 23, 2017
Explanation:
First note that:
#1/(sqrt(n+1)+sqrt(n)) = (sqrt(n+1)-sqrt(n))/((sqrt(n+1)+sqrt(n))(sqrt(n+1)-sqrt(n))#
#color(white)(1/(sqrt(n+1)+sqrt(n))) = (sqrt(n+1)-sqrt(n))/((n+1)-n)#
#color(white)(1/(sqrt(n+1)+sqrt(n))) = sqrt(n+1)-sqrt(n)#
So:
#1/(sqrt(144)+sqrt(145))+1/(sqrt(145)+sqrt(146))+...+1/(sqrt(168)+sqrt(169))#
#=(sqrt(145)-sqrt(144))+(sqrt(146)-sqrt(145))+...+(sqrt(169)-sqrt(168))#
#=sqrt(169)-sqrt(144)#
#=13-12#
#=1#