Question

設(shè)二項(xiàng)式(3

3	x

+

1

x

)n的展開(kāi)式中各項(xiàng)系數(shù)和為p，各項(xiàng)的二項(xiàng)式系數(shù)和為s，若p+s=272，則n等于

4

．

Answer 1

分析：各項(xiàng)系數(shù)之和為P．即x=1時(shí)，P=4ⁿ，二項(xiàng)系數(shù)和為2ⁿ，從而代入條件即可求．

解答：解：由題意各項(xiàng)系數(shù)之和為P．即x=1時(shí)，P=4ⁿ，二項(xiàng)系數(shù)和為2ⁿ，
∴4ⁿ+2ⁿ=272，，∴2ⁿ=16，∴n=4，
故答案為4

點(diǎn)評(píng)：本題主要考查二項(xiàng)式中系數(shù)問(wèn)題，應(yīng)注意區(qū)分各項(xiàng)系數(shù)和與二項(xiàng)式系數(shù)和．