So from what I've found using excel this inequality wholes true where n > 2 where n is in naturals
I have 2 questions. How would I do this not using excel? Would the easiest way be to use a calculator? I dont understand how else I would solve this equation (by maybe setting them equal and coming up with an answer between 2 and 3 and then rounding up).
In adition, I'm pretty sure the way to solve this is by using induction. So for my base case let N = 3. Then I will let n = k + 1 and need to show that 5^(k+1) + 6^(k+1) > 7^(k+1).
I can manipulate this into saying (5^k * 5) + (6^k * 6) < (7^k * 7). But where would I go from here? I know I need to somehow use my IH but don't quote know how.
Thanks for the help.