GO Classes Scholarship 2023 | Test | Question: 26

Answer 1

$\sum_{i=1}^{10} \sum_{j = 1}^{10} (i*j) = \sum_{i=1}^{10} i* \sum_{j = 1}^{10} j = \sum_{i=1}^{10} i * 55 = 55* \sum_{i=1}^{10} i = 55 * 55 = 3025$

Answer 2

$\sum_{i=1}^{n} i = \frac{n * (n+1)}{2}$.

$\sum_{i=1}^{10} i = \frac{10 * 11}{2} = 55$.

$sum = 1 * 1 + 1 * 2 + … + 1 * 10 + 2 * 1 + 2 * 2 + … + 2 * 10 + … + 10 * 1 + 10 * 2 + … + 10 * 10$.

$sum = 1 * (1 + 2 + .. + 10) + 2 * (1 + 2 + .. + 10) + … + 10 * (1 + 2 + .. + 10)$.

$sum = 1 * (55) + 2 * (55) + … + 10 * (55)$.

$sum = 55 * (1 + 2 + .. + 10)$.

$sum = 55 * 55$.

$sum = 3025$.

Answer 3

Initially $sum = 0$,

for every i, j will run for 10 times.

If we notice then

$sum = 1*1 + 1*2 + \dots +1*10 + 2*1 + 2*2 + \dots + 2*10 + 3*1 + \dots + 10*1 + \dots + 10*10$

$sum = 1(1+2 + \dots + 10) + 2(1+2+\dots+10) + \dots + 10(1+2+\dots+10)$

$sum = 1*55 + 2*55 + 3*55 + \dots + 10*55$

$sum = 55*(1+2+\dots +10)$

$sum = 55*55 = 3025$