friends problems

Posted on November 10, 2015 by neelanjan mondal

A class has 100 students .Let $a_i$ $\leq$ i $\leq$ 100, denotes the number of friends the i – th student has in the class . For each 0 $\leq$ j $\leq$ 99 , let $c_j$ denote the number of students having atleast j friends . Show that $\sum_{i=1}^m a_i$ = $\sum_{i=0}^n c_i$ , where m = 100 and n = 99.