Câu 21. Khái triển \({\left( {3x + 1} \right)^{10}}\) cho tới x ³ .

Giải

Ta có:

\(\eqalign{
& {\left( {3x + 1} \right)^{10}} = \sum\limits_{k = 0}^{10} {C_{10}^k{{\left( {3x} \right)}^k} = 1 + C_{10}^1\left( {3x} \right) + C_{10}^2{{\left( {3x} \right)}^2} + C_{10}^3{{\left( {3x} \right)}^3} + . . . } \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1 + 30x + 405{x^2} + 3240{x^3} + . . . \cr} \)