ABCD is a square of length \( a, a \in N, a1 \). Let \( \mathrm{L}_{1}, \mathrm{~L}_{2}, \mathrm{~L}_{3}, \ldots \) be points on
\( \mathrm{P} \) BC such that \( B L_{1}=L_{1} L_{2}=L_{2} L_{3}=\ldots=1 \) and \( \mathrm{M}_{1}, \mathrm{M}_{2}, \mathrm{M}_{3}, \ldots \) be points on
W \( C D \) such that \( C M_{1}=M_{1} M_{2}=M_{2} M_{3}=\ldots=1 \). Then \( \Sigma\left(A L_{n}^{2}+L_{n} M_{n}^{2}\right) \) is equal to
(a) \( \frac{1}{2} a(a-1)^{2} \)
(b) \( \frac{1}{2} a(a-1)(4 a-1) \)
(c) \( \frac{1}{2}(a-1)(2 a-1)(4 a-1) \)
(d) none of these
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