问题 解答题
计算题:
(1)复数z=i+i2+i3+i4
(2)(
C2100
+
C97100
A3101

(3)
C33
+
C34
+…+
C310
答案

(1)原式=i-1-i+1=0

(2)原式=(

C2100
+
C3100
A3101
=
C3101
÷
A3101
=
A3101
A33
÷
A3101
=1÷
A33
=
1
6

(3)原式=

C33
+
C45
-
C44
+
C46
-
C45
+…+
C411
-
C410
=
C411
=330.

另一方法:原式=

C44
+
C34
+
C35
+…+
C310
=
C35
+…
C310
=
C46
+
C36
+…+
C310
=…=
C410
+
C310
=
C411
=330

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