Question

11．求代數(shù)式（$\root{6}{x}$+$\frac{1}{\root{6}{x}}$）ⁿ的展開式．

Answer 1

分析 由條件利用二項(xiàng)式定理求得代數(shù)式（$\root{6}{x}$+$\frac{1}{\root{6}{x}}$）ⁿ的展開式．

解答 解：代數(shù)式（$\root{6}{x}$+$\frac{1}{\root{6}{x}}$）ⁿ =${C}_{n}^{0}$•${x}^{\frac{n}{6}}$+${C}_{n}^{1}$•${x}^{\frac{n-1}{6}}$•${x}^{\frac{1}{6}}$+${C}_{n}^{2}$•${x}^{\frac{n-2}{6}}$•${x}^{-\frac{2}{6}}$+…+${C}_{n}^{n}$•${x}^{-\frac{n}{6}}$
${C}_{n}^{0}$•${x}^{\frac{n}{6}}$+${C}_{n}^{1}$•${x}^{\frac{n-2}{6}}$+${C}_{n}^{2}$•${x}^{\frac{n-4}{6}}$+…+${C}_{n}^{n}$•${x}^{-\frac{n}{6}}$．

點(diǎn)評 本題主要考查二項(xiàng)式定理的應(yīng)用，二項(xiàng)展開式的通項(xiàng)公式，屬于基礎(chǔ)題．