JEE Advance - Mathematics (1985 - No. 15)
Use method of mathematical induction $${2.7^n} + {3.5^n} - 5$$ is divisible by $$24$$ for all $$n > 0$$
Base Case: Verify the statement for n = 1.
Inductive Hypothesis: Assume the statement is true for n = k.
Inductive Step: Prove the statement is true for n = k+1, using the inductive hypothesis.
Base Case: Verify the statement for n = 0.
The statement is not provable by mathematical induction.