1. Tardigrade
  2. Question
  3. Mathematics
  4. For n ∈ N, 10n-2 ≥ 81 n, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. For $n \in N, 10^{n-2} \geq 81\, n$, is

ManipalManipal 2008

Solution:

Let $P(n): 10^{n-2} \geq 81\, n$
For $n=4,\,\,\,10^{2} ⪈ 81 \times 4$
For $n=5,\,\,\,10^{3} \ge 81 \times 5$
Hence, by mathematical induction for $n \geq 5$,the proposition is true.