Find the value of:

(1³/1) + (1³+2³)/(1+3) + (1³+2³+3³)/(1+3+3) + ... up to 8 terms.

The nth term is:

T_n = (1³ + 2³ + 3³ + ... + n³) / (1 + 3 + 3 + ... + 3)

Using the formula:

1³ + 2³ + ... + n³ = [n(n+1)/2]²

Denominator:

1 + 3(n−1) = 3n−2

Substituting values from n = 1 to 8 and simplifying gives:

S = 72

Final Answer

Option (4) 72