a) Khai triển (1 + x)10. b) (1,1)10 và 2.

a) ${\left(1+x\right)}^{10}=C_{10}^0{1}^{10}+C_{10}^1{1}^{9}x+C_{10}^2{1}^8{x}^2+\mathrm{...}+C_{10}^{9}1x^9+C_{10}^{10}{x}^{10}$

$=1+C_{10}^{1}x+C_{10}^2{x}^2+\mathrm{...}+C_{10}^9{x}^9+x^{10}.$

b) Áp dụng câu a) ta có:

${\left(\mathrm{1,1}\right)}^{10}={\left(1+\mathrm{0,1}\right)}^{10}$

$=1+C_{10}^1\mathrm{.0,1}+C_{10}^2{\left(\mathrm{0,1}\right)}^2+\mathrm{...}+C_{10}^9{\left(\mathrm{0,1}\right)}^9+{\left(\mathrm{0,1}\right)}^{10}>1+C_{10}^1\mathrm{.0,1}=2.$