IIT-JEE 1982Question 1
In a certain test, $a_i$ students gave wrong answers to at least $i$ questions, where $i=1,2,\ldots,k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is ______.
Permutation and Combination
Answer$a_1+a_2+\cdots+a_k$
Solution
Exactly $i$ wrong answers were given by $a_i-a_{i+1}$ students ($a_{k+1}=0$), so the total is $\sum_{i=1}^k i(a_i-a_{i+1})=a_1+a_2+\cdots+a_k$.