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Mathematical Induction — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSMathematical Induction3 Marks
Question
If P(n) is the statement "2n ≥ 3n" and if P(r) is true, prove that P(r + 1) is true.
✓

Answer

P(n): 2n ≥ 3n
Given that P(r) is true
⇒ 2r ≥ 3r
Multiplying both sides by 2,
2.2r ≥ 2.3r
2r+1 ≥ 6r
2r+1 ≥ 3r + 3r
2r+1 ≥ 3 + 3r, [Since 3r ≥ 3 ⇒ 3r + 3r ≥ 3 + 3r]
2r+1 ≥ 3r(r + 1)
⇒ P(r + 1) is true.

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