Discussion

Explanation:

(111)₂ = 1 × 2² + 1 × 2¹ + 1 = 2³– 1.

Similarly, (222)₃ = 3³– 1,

… and so on till

(FFF)16 = 16³ – 1.

∴ (111)₂ + (222)₃ + (333)₄ + (444)₅ + … +  (FFF)₁₆ = (2³- 1) + (3³ - 1) + (4³- 1) + … + (16³- 1) 

= (2³ + 2³ + … + 16³) - 15

= (1³ + 2³ + 2³ + … + 16³) - 16

${\left[\frac{16\left(16+1\right)}{2}\right]}^2$ - 16

Hence, option (c).

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