问题
选择题
《棋盘上的米粒》故事中,皇帝往棋盘的第1格中放1粒米,第2格中放2粒米,在第3格上加倍至4粒,…,依此类推,每一格均是前一格的双倍,那么他在第12格中所放的米粒数是( )
A.22粒
B.24粒
C.211粒
D.212粒
答案
设第n格中放的米粒数是an,则
a1=1,
a2=a1×2,
a3=a2×2=a1×22,
…
an=a1×2n-1,
∴a12=a1×211=211.
故选C.
《棋盘上的米粒》故事中,皇帝往棋盘的第1格中放1粒米,第2格中放2粒米,在第3格上加倍至4粒,…,依此类推,每一格均是前一格的双倍,那么他在第12格中所放的米粒数是( )
A.22粒
B.24粒
C.211粒
D.212粒
设第n格中放的米粒数是an,则
a1=1,
a2=a1×2,
a3=a2×2=a1×22,
…
an=a1×2n-1,
∴a12=a1×211=211.
故选C.
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