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Statement -1 for all natural numbers n ,...

Statement -1 for all natural numbers n , `2.7^(n)+3.5^(n)-5` is divisible by 24.
Statement -2 if f(x) is divisible by x, then `f(x+1)-f(x)` is divisible by `x+1,forall x in N`.

A

Statement -1 is true , Statement -2 is true, Statement -2 is correct explanation for Statement -2

B

Statement -1 is true , Statement -2 is true , Statement -2 is not correct explanation for Staement -2

C

Statement -1 is true , Statement -2 is false

D

Statement -1 is false , Statement - 2 is true.

Text Solution

AI Generated Solution

To solve the problem using mathematical induction, we will focus on Statement 1: "For all natural numbers n, \(2 \cdot 7^n + 3 \cdot 5^n - 5\) is divisible by 24." ### Step-by-Step Solution **Step 1: Base Case (n = 1)** We start by checking the base case where \(n = 1\). \[ ...
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