3-100-2-100-4-100-which-is-greater-Give-proof-

Question Number 191443 by MATHEMATICSAM last updated on 24/Apr/23

(3^{100} + 2^{100}), 4^{100} which is greater ?

Give proof .

Answered by Frix last updated on 24/Apr/23

4^{100} = 2^{200} > 2^{100} + 3^{100}

2^{200} - 2^{100} > 3^{100}

2^{100} (2^{100} - 1) > 3^{100}

2^{100} - 1 > {(\frac{3}{2})}^{100} which is obvious

Answered by mehdee42 last updated on 24/Apr/23

4^{100} = 16^{50} > 13^{50} = {(4 + 9)}^{50} > 4^{50} + 9^{50}

\Rightarrow 4^{100} > 2^{100} + 3^{100}

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