Questão 2318444

\(\binom{100}{0}^{2}\) + \(\binom{100}{1}^{2}\) + ... + \(\binom{100}{100}^{2}\) = \(\binom{200}{100}^{2}\)

\(\binom{100}{39}\) + \(\binom{100}{40}\) = \(\binom{101}{40}\)

2 x 1 x \(\binom{100}{2}\) + 3 x 2 x \(\binom{100}{3}\) + 4 x 3 x \(\binom{100}{4}\) + ... + 100 x 99 x \(\binom{100}{100}\) = 9900 x 2⁹⁸

\(\binom{100}{1}\) + 2 x \(\binom{100}{2}\) + 3 x \(\binom{100}{3}\) + ... + 100 x \(\binom{100}{100}\) = 100 x 2⁹⁹

1 - \(\binom{100}{1}\) + \(\binom{100}{2}\) - \(\binom{100}{3}\) + ... + \(\binom{100}{100}\) = 0