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If P(n):2nltn!,ninN then P(n) is true fo...

If `P(n):2nltn!,ninN` then P(n) is true for all `n≥` . . . . . . . . . .

Text Solution

Verified by Experts

Given that `P(n):2nltn!,ninN`
For n=1, `2lt!` [false]
For n=2, `2xx2lt!4lt2` [false]
For n=3, `2xx3lt!`
`6lt3!`
`6lt3xx2xx1`
`(6lt6)` [false]
For n=4, `2xx4lt4!`
`8lt4xx3xx2xx1`
`(8lt24)` [true]
`For n=5, 2xx5lt5!`
`10lt5xx4xx3xx2xx1`
`(10lt120)` [true]
Hence, P(n) is for all `nle4`. [true]
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