IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - Prove that for allintegers n2, 2n-1 (3n + 4n) >7n

sekara0809

Prove that for allintegers n

2, 2^n-1 (3ⁿ + 4ⁿ) >7ⁿ

indr12365

Tag it expert....
I think something from mathemetical induction could solve it

hsbhatt

There is an inequality that is known as the Power Mean Inequality. The version we will use here is: $\left (\frac{a^n+b^n}{2} \right)^\frac{1}{n} \ge \frac{a+b}{2}$

Here a =3, b =4and you get $2^{n-1} (3^n+4^n) \ge (3+4)^n = 7^n$

PS: Can u try using Chebyshev's Inequality for this one?

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