1-90C101+902C102-903C103+…+(-1)k90kC10k+…+9010C1010除以88的余数是()A.-87B.87C.-1D.1-数学

题目简介

1-90C101+902C102-903C103+…+(-1)k90kC10k+…+9010C1010除以88的余数是()A.-87B.87C.-1D.1-数学

题目详情

1-90C101+902C102-903C103+…+(-1)k90kC10k+…+9010C1010除以88的余数是(  )
A.-87B.87C.-1D.1
题型:单选题难度:中档来源:不详

答案

1-90C101+902C102-903C103+…+(-1)k90kC10k+…+9010C1010
=(1-90)10
=8910
=(1+88)10
=C100+C10188+…+C109×889+C10108810
=1+C10188+…+C109×889+C10108810
所以除以88的余数为1
故选D

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