The Total solution for NCERT class 6-12
If P (n) is the statement “2n ≥3n”, and if P (r) is true, prove that P (r + 1) is true.
Given:
P (n) = “2n ≥ 3n” and p(r) is true.
We have, P (n) = 2n ≥ 3n
Since, P (r) is true
So,
2r≥ 3r
Now, let’s multiply both sides by 2
2×2r≥ 3r×2
2r + 1≥ 6r
2r + 1≥ 3r + 3r [since 3r>3 = 3r + 3r≥3 +3r]
∴ 2r + 1≥ 3(r + 1)
Hence, P (r + 1) is true.