问题 填空题
C02013
+
C22013
+
C42013
+
C62013
+…+
C20122013
=______.
答案

∵(1-1)2013=

C02013
-
C12013
+
C22013
-…+
C20122013
-
C20132013
=0,①

(1+1)2013=

C02013
+
C12013
+
C22013
+…+
C20122013
-
C20132013
=22013,②

①+②得:

2(

C02013
+
C22013
+
C42013
+…+
C20122013
)=22013

C02013
+
C22013
+
C42013
+…+
C20122013
=22012

故答案为:22012

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