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JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Let n≥5n \geq 5 be an integer. If 9n−8n−1=64α9^n-8 n-1=64 \alpha and 6n−5n−1=25β6^n-5 n-1=25 \beta, then α−β\alpha-\beta is equal to
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Correct option: C
nC3(8−5)+nC4(82−52)+…+nCn(8n−2−5n−2)^n{C_3}(8 - 5){ + ^n}{C_4}\left( {{8^2} - {5^2}} \right) + \ldots { + ^n}{C_n}\left( {{8^{n - 2}} - {5^{n - 2}}} \right)
Option C is correct because it represents the difference between the series expansions of (1+8)^n and (1+5)^n, after accounting for the initial terms and dividing by 64 and 25 respectively.

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