In a certain test,a_i students gave wrong ans | vedclass

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(B) Let $N_i$ be the number of students who gave exactly $i$ wrong answers. Since no student gave more than $k$ wrong answers,the total number of wron

Vedclass · Accepted Answer

$a_1 + a_2 + a_3 + \dots + a_k$

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(B) Let $N_i$ be the number of students who gave exactly $i$ wrong answers. Since no student gave more than $k$ wrong answers,the total number of wrong answers is $\sum_{i=1}^{k} i \cdot N_i$. We are given that $a_i$ is the number of students who gave at least $i$ wrong answers. Thus,$a_i = N_i + N_{i+1} + \dots + N_k$. This implies $N_i = a_i - a_{i+1}$ for $i The total number of wrong answers is $1 \cdot N_1 + 2 \cdot N_2 + \dots + k \cdot N_k$. Substituting the values of $N_i$: $= 1(a_1 - a_2) + 2(a_2 - a_3) + \dots + (k-1)(a_{k-1} - a_k) + k(a_k)$ $= a_1 + (2-1)a_2 + (3-2)a_3 + \dots + (k-(k-1))a_k$ $= a_1 + a_2 + a_3 + \dots + a_k$.

In a certain test,$a_i$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, \dots, k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

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