[JEE Advanced 1980] given n 4 10 n for a fixed integer n 2 prove n 1
Given $n^4<10^n$ for a fixed integer $n\ge2$, prove $(n+1)^4<10^{n+1}$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Answer: Proved.
$\left(\frac{n+1}n\right)^4\le\left(\frac32\right)^4=\frac{81}{16}<10$, so $(n+1)^4<10\,n^4<10\cdot10^n=10^{n+1}$.
JEE Advanced 1980 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.