Question -
Answer -
Given:
P (n) = тАЬ2n┬атЙе 3nтАЭ and p(r) is true.
We have,┬аP (n) = 2n┬атЙе 3n
Since, P (r) is true
So,
2rтЙе┬а3r
Now, letтАЩs multiply both sides by 2
2├Ч2rтЙе┬а3r├Ч2
2r + 1тЙе┬а6r
2r + 1тЙе┬а3r + 3r [since 3r>3 = 3r + 3rтЙе3 +3r]
тИ┤ 2r + 1тЙе┬а3(r + 1)
Hence, P (r + 1) is true.