Chứng minh rằng C 0 5 - C 1 5 + C 2 5 - C 3 5 + C 4 5 - C 5 5 = 0

Ta có: \(C_5^0 - C_5^1 + C_5^2 - C_5^3 + C_5^4 - C_5^5\)

\( = C_5^0{.1^5} + C_5^1{.1^4}.{\left( { - 1} \right)^1} + C_5^2{.1^3}.{\left( { - 1} \right)^2} + C_5^3{.1^2}.{\left( { - 1} \right)^3} + C_5^4{.1^1}.{\left( { - 1} \right)^4} + C_5^5.{\left( { - 1} \right)^5}\)

= (1 – 1)⁵ = 0 (nhị thức Newton).