Let S_K = (1 + 2 + … + K)/K and Σ_(j=1)ⁿ S_j² = n/A(Bn² + Cn + D)… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 8 April, Shift 1Sum of Series

Let $S_K = \frac{1 + 2 + \dots + K}{K}$ and $\sum_{j=1}^{n} S_j^2 = \frac{n}{A}\left(Bn^2 + Cn + D\right)$ , where $A, B, C, D \in \mathbb{N}$ and $A$ has the least value. Then:

A
$A + B$ is divisible by $D$
B
$A + B = 5(D - C)$
C
$A + C + D$ is not divisible by $B$
D
$A + B + D$ is divisible by $5$

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