Question

Calcule o valor das expressões usando as propriedades do triângulo de pascal.
A) (5/0)+(5/1)+(5/2)+(5/3)+(5/4)+(5/5) =

B) (6/1)+(6/2)+...+(6/5)+(6/6) =

C) (9/5)+(9/4) =

D) (8/0)+(8/1)+(8/2)+(8/3) =

Answer 1

Explicação passo-a-passo:

${2}^{5} = 32 \\ \\ {2}^{6} - \binom{6}{0} = 64 - \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{(1) \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 64 - 1 = 63 \\ \\ \binom{9}{5} = \binom{9}{4} \: \: \: \: logo \: \: \: \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(5 \times 4 \times 3 \times 2 \times 1) \times (4 \times 3 \times 2 \times 1)} \times 2 =252$

$\binom{8}{0} = 1 \\ \binom{8}{1} = 8 \\ \binom{8}{2} = 28 \\ \binom{8}{3} = 56 \\ 1 + 28 + 8 + 56 = 93$