JEE Advance - Mathematics (1980 - No. 12)
Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$
The statement is false and cannot be proven.
The statement is true for all positive integers n >= 2.
We must show that $\frac{(n+1)^4}{n^4} < 10$.
The given inequality ${n^4} < {10^n}$ is irrelevant to proving ${\left( {n + 1} \right)^4} < {10^{n + 1}}.$
The condition n >= 2 is unnecessary.
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