[JEE Main 2002] use induction to show 25 n 1 24n 5735 is divisible by 24 2
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
· 2d ago
▲ 0
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.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.