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Statement -1 For each natural number n,(...

Statement -1 For each natural number `n,(n+1)^(7)-n^7-1` is divisible by 7.
Statement -2 For each natural number `n,n^7-n` is divisible by 7.

A

Statement-1 is false , Statement-2 is true

B

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

C

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

D

Statement-1 is true , Statement-2 is false

Text Solution

AI Generated Solution

To solve the problem using mathematical induction, we will analyze both statements separately. ### Statement 2: For each natural number \( n \), \( n^7 - n \) is divisible by 7. **Base Case:** We start with \( n = 1 \): \[ 1^7 - 1 = 1 - 1 = 0 ...
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