Question

Помогите пжж не могу понять вообще

Answer 1

Ответ:

1024

Объяснение:

Действуем по формуле:

C₁₀⁰ = $\frac{10!}{0!(10-0)!}$ = 1

С₁₀¹ = $\frac{10!}{1!(10-1)!}$ = 10! / 9! = (10 * 9!) / 9! = 10

С₁₀² = $\frac{10!}{2!(10-2)!}$ = 10! / (2! * 8!) = (10 * 9 * 8!) / (2! * 8!) = 90 / 2! = 90 / 2 = 45

C₁₀³ = $\frac{10!}{3!(10-3)!}$ = 10! / (3! * 7!) = (10 * 9 * 8 * 7!) / (3! * 7!) = 10 * 9 * 8 / 3*2 =

= 120

C₁₀⁴ = $\frac{10!}{4!(10-4)!}$ = 10! / (4! * 6!) = (10 * 9 * 8 * 7 * 6!) / (4! * 6!) =                                    

= 5040 / 4 * 3 * 2 * 1 = 5040 / 24 = 210

C₁₀⁵ = $\frac{10!}{5!(10-5)!}$ = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5!) =

= (10 * 9 * 8 * 7 * 6) / 5! = 30240 / 120 = 252

C₁₀⁶ = $\frac{10!}{6!(10-6)!}$ = 10! / (6! * 4!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7 * 6!) / (4! * 6!) =                                    

= 5040 / 4 * 3 * 2 * 1 = 5040 / 24 = 210

C₁₀⁷ = $\frac{10!}{7!(10-7)!}$ = 10! / (7! * 3!) = 10! / (3! * 7!) = (10 * 9 * 8 * 7!) / (3! * 7!) =

= 10 * 9 * 8 / 3*2 = 120

C₁₀⁸ = $\frac{10!}{8!(10-8)!}$ = 10! / (8! * 2!) = 10! / (2! * 8!) = (10 * 9 * 8!) / (2! * 8!) = 90 / 2! =

= 90 / 2 = 45

C₁₀⁹ = $\frac{10!}{9!(10-9)!}$ = 10! / 9! = (10 * 9!) / 9! = 10

C₁₀¹⁰ = $\frac{10!}{10!(10-10)!}$ = 1

Отсюда сумма слагаемых равна:

1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 =

= 2*1 + 2*10 + 2*45 + 2*120 + 2*210 + 252 =

= 2 + 20 + 90 + 240 + 420 + 252 = 1024