- #1

idobido

- 10

- 0

- Homework Statement
- not done

- Relevant Equations
- Bernoulli's inequality

Newton's Binomial

Taylor expansion

let ##k \in\mathbb{N},## Show that there is ##i\in\mathbb{N} ##s.t ##\ \left(1-\frac{1}{k}\right)^{i}-\left(1-\frac{2}{k}\right)^{i}\geq \frac{1}{4} ##

I tried to use Bernoulli's inequality and related inequality for the left and right expression but i the expression smaller than 1/4 for any i or k.

I also tried Newton's Binomial Theorem, Taylor expansion with no success.

I tried to use Bernoulli's inequality and related inequality for the left and right expression but i the expression smaller than 1/4 for any i or k.

I also tried Newton's Binomial Theorem, Taylor expansion with no success.

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