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Using principle of MI prove that 2.7^n+3...

Using principle of MI prove that `2.7^n+3.5^n-5` is divisible by 24

Text Solution

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Given expression is.
`2*7^n+3*5^n-5`
When `n = 1`, given expression is,
`2*7+3*5-5 = 12+15-5 = 24`
So, for `n=1`, given expession is divisible by `24`.
Let for any `k in N`, given expression is divisible by `24`.
Then, `2*7^k+3*5^k-5 = 24c`, where `c` is a natural number.
`=>3*5^k = 24c-2*7^k+5->(1)`
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