Пжж не могу понять вообще

Ответ:
1024
Объяснение:
Действуем по формуле:
C₁₀⁰ = = 1
С₁₀¹ = = 10! / 9! = (10 * 9!) / 9! = 10
С₁₀² = = 10! / (2! * 8!) = (10 * 9 * 8!) / (2! * 8!) = 90 / 2! = 90 / 2 = 45
C₁₀³ = = 10! / (3! * 7!) = (10 * 9 * 8 * 7!) / (3! * 7!) = 10 * 9 * 8 / 3*2 =
= 120
C₁₀⁴ = = 10! / (4! * 6!) = (10 * 9 * 8 * 7 * 6!) / (4! * 6!) =                                    
= 5040 / 4 * 3 * 2 * 1 = 5040 / 24 = 210
C₁₀⁵ = = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5!) =
= (10 * 9 * 8 * 7 * 6) / 5! = 30240 / 120 = 252
C₁₀⁶ = = 10! / (6! * 4!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7 * 6!) / (4! * 6!) =                                    
= 5040 / 4 * 3 * 2 * 1 = 5040 / 24 = 210
C₁₀⁷ = = 10! / (7! * 3!) = 10! / (3! * 7!) = (10 * 9 * 8 * 7!) / (3! * 7!) =
= 10 * 9 * 8 / 3*2 = 120
C₁₀⁸ = = 10! / (8! * 2!) = 10! / (2! * 8!) = (10 * 9 * 8!) / (2! * 8!) = 90 / 2! =
= 90 / 2 = 45
C₁₀⁹ = = 10! / 9! = (10 * 9!) / 9! = 10
C₁₀¹⁰ = = 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