[tex] {(6 + 12 + 18 + ... + 300)}^{3} \div (3 + 6 + 9 + ... + 150)[/tex]
[tex] ={ [2(3 + 6 + 9 + ... + 150)]}^{3} \div (3 + 6 + 9 + ... + 150)[/tex]
[tex] = [ {2}^{3} {(3 + 6 + 9 + ... + 150)}^{3} ] \div (3 + 6 + 9 + ... + 150)[/tex]
[tex] = 8 {(3 + 6 + 9 + ... + 150)}^{3 - 1} [/tex]
[tex] = 8{(3 + 6 + 9 + ... + 150)}^{2} [/tex]
[tex] = 8{[3(1 + 2 + 3 + ... + 50)]}^{2} [/tex]
[tex] = 8{[3 \times \frac{50(50 + 1)}{2} ]}^{2} [/tex]
[tex] = 8{ (3 \times \frac{50 \times 51}{2} )}^{2} [/tex]
[tex] = 8{(3 \times 25 \times 51)}^{2} [/tex]
[tex] = 8 {(75 \times 51)}^{2} [/tex]
[tex] = 8 \times {3825}^{2} [/tex]
[tex] = 8 \times 14630625[/tex]
[tex] = 117045000[/tex]
