How do I prove that the next expression is true for every natural n that is above 1: thanks
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What have you tried? Do you know how induction works?
n=k: n=k+1: no idea how to continue
By observation I would start with the given inequality which holds: $\displaystyle 2^{k-1}(2^k+3^k)>5^k$ Multiply both sides with a factor 5 and proceed.
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