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Sequences and Series question

2023 · 8 Apr · Shift 1 · Q35

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PYQ Library
JEE Main
Mathematics
Sequences and Series
2023 · 8 Apr · Shift 1 · Q35

Sequences and Series question

2023 · 8 Apr · Shift 1 · Q35

JEE MainMathematicsSequences and SeriesMCQ+4 / −1

Let

S_{K}=\frac{1+2+\ldots+K}{K}

and

\sum_{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right)

, where

A, B, C, D \in \mathbb{N}

and

A

has least value. Then

A
$A+B+C+D$ is divisible by 5
B
$A+C+D$ is not divisible by $B$
C
$A+B=5(D-C)$
D
$A+B$ is divisible by $\mathrm{D}$

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