SOLUTION: Use the method of mathematical induction to establish the following 1. 1+3+5+...+(2n-1)=2^n 2. 7^(2n+1) is divided by 8 3. 3^(4n+2) + 2.4^(3n+1) is exactly divisible by 7

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Question 1082083: Use the method of mathematical induction to establish the following
1. 1+3+5+...+(2n-1)=2^n
2. 7^(2n+1) is divided by 8
3. 3^(4n+2) + 2.4^(3n+1) is exactly divisible by 7
4. n^(4) + 4n^(2) + 11 is a multiple of 16 for all odd positive integer n.
Answer by ikleyn(52776) (Show Source):
You can put this solution on YOUR website!
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Use the method of mathematical induction to establish the following

1. 1+3+5+...+(2n-1)=2^n THIS FORMULA IS WRONG 2. 7^(2n+1) is divided by 8 THIS STATEMENT IS WRONG 3. 3^(4n+2) + 2.4^(3n+1) is exactly divisible by 7 THIS STATEMENT IS WRONG (I checked it at n = 1, 2, 3, 4, 5) 4. n^(4) + 4n^(2) + 11 is a multiple of 16 for all odd positive integer n.