IME 2021 — Questão 10 · Binômio de Newton

Alternativas

1. A

   ${\left(\frac{100}{0}\right)}^2$ + ${\left(\frac{100}{1}\right)}^2$ + ... + ${\left(\frac{100}{100}\right)}^2$ = ${\left(\frac{200}{100}\right)}^2$

2. B

   $\left(\frac{100}{39}\right)$ + $\left(\frac{100}{40}\right)$ = $\left(\frac{101}{40}\right)$

3. C

   2 x 1 x $\left(\frac{100}{2}\right)$ + 3 x 2 x $\left(\frac{100}{3}\right)$ + 4 x 3 x $\left(\frac{100}{4}\right)$ + ... + 100 x 99 x $\left(\frac{100}{100}\right)$ = 9900 x 2⁹⁸

4. D

   $\left(\frac{100}{1}\right)$ + 2 x $\left(\frac{100}{2}\right)$ + 3 x $\left(\frac{100}{3}\right)$ + ... + 100 x $\left(\frac{100}{100}\right)$ = 100 x 2⁹⁹

5. E

   1 - $\left(\frac{100}{1}\right)$ + $\left(\frac{100}{2}\right)$ - $\left(\frac{100}{3}\right)$ + ... + $\left(\frac{100}{100}\right)$ = 0