In a certain test,{a_i} students gave wrong a | vedclass

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(B) Let $x_j$ be the number of students who gave exactly $j$ wrong answers,where $1 \le j \le k$.The total number of wrong answers is given by $\sum_{

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${a_1} + {a_2} + {a_3} + ... + {a_k}$

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(B) Let $x_j$ be the number of students who gave exactly $j$ wrong answers,where $1 \le j \le k$.The total number of wrong answers is given by $\sum_{j=1}^{k} j \cdot x_j$.We are given that ${a_i}$ is the number of students who gave at least $i$ wrong answers.Thus,${a_i} = \sum_{j=i}^{k} x_j$.This implies ${a_i} - {a_{i+1}} = x_i$ for $1 \le i The total number of wrong answers is $\sum_{i=1}^{k} i \cdot x_i = 1(x_1) + 2(x_2) + ... + k(x_k)$.Substituting $x_i = {a_i} - {a_{i+1}}$:Total $= 1({a_1} - {a_2}) + 2({a_2} - {a_3}) + 3({a_3} - {a_4}) + ... + (k-1)({a_{k-1}} - {a_k}) + k({a_k})$.Expanding this sum:Total $= {a_1} - {a_2} + 2{a_2} - 2{a_3} + 3{a_3} - 3{a_4} + ... + (k-1){a_{k-1}} - (k-1){a_k} + k{a_k}$.Total $= {a_1} + (-1+2){a_2} + (-2+3){a_3} + ... + (-(k-1)+k){a_k}$.Total $= {a_1} + {a_2} + {a_3} + ... + {a_k}$.

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

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