(1)2×(-3)3-4×(-3)+15; (2)(1/2-5/9+7/12)×(-36); (3)已知1+2+3+…+31+32+33=17×33,求 1-3+2-6+3-9+4-12+…+31-93+32-96+33-99的值.

问题描述:

(1)2×(-3)3-4×(-3)+15;
(2)(

1
2
-
5
9
+
7
12
)×(-36);
(3)已知1+2+3+…+31+32+33=17×33,求 1-3+2-6+3-9+4-12+…+31-93+32-96+33-99的值.

(1)2×(-3)3-4×(-3)+15
=2×(-27)-4×(-3)+15
=-54-(-12)+15
=-54+12+15
=-54+27
=-(54-27)
=-27;
(2)(

1
2
-
5
9
+
7
12
)×(-36)
=(-36)×
1
2
+(-36)×(-
5
9
)+(-36)×
7
12

=-18+20+(-21)
=[-18+(-21)]+20
=-39+20
=-(39-20)
=-19;
(3)∵1+2+3+…+31+32+33=17×33,
∴1-3+2-6+3-9+4-12+…+31-93+32-96+33-99
=-2(1+2+3+…+31+32+33)
=-2×17×33
=-1122.