[JEE Main 2002] Use induction to show $25^{n+1}-24n+5735$ is divisible by $24^2$ for all $n=1,2,\dots$.
Use induction to show $25^{n+1}-24n+5735$ is divisible by $24^2$ for all $n=1,2,\dots$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: Proved (divisible by $576$).
Base $n=1$: $625-24+5735=6336=11\cdot576$. The step difference is $25^{n+1}\cdot24-24=24(25^{n+1}-1)$, and $25^{n+1}-1$ is divisible by $24$, so the increment is divisible by $24^2$.
JEE Main 2002 · Binomial Theorem — verified solution by the Vidaara Team.
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