(1³ + 2³ + 3³ + .............. + n³)/(1 + 2 + 3 + ............... + n) = 55 হলে, n এর মান কত?

(1³ + 2³ + 3³ + .............. + n³)/(1 + 2 + 3 + ............... + n) = 55
{n(n + 1)/2}²/{n(n + 1)/2} = 55
n(n + 1)/2 = 55
n(n + 1) = 110
n² + n - 110 = 0
n² + 11n - 10n - 110 = 0
n(n + 11) - 10 (n + 11 )= 0
(n + 11)(n - 10) = 0
হয়
n + 11 = 0
n = - 11 [গ্রহণযোগ্য নয়]
অথবা
n - 10 = 0
n = 10