A-A+

神机妙算(能简算的要写出简算过程)(1)112+216+3112+…+101110=(2)(

2022-08-14 02:35:45 问答库 阅读 200 次

问题详情

神机妙算(能简算的要写出简算过程)
(1)11

2

+21

6

+31

12

+…+101

110

=
(2)(15

7

×7

12

+63

4

1

2

+1

4

)÷(1-1

11

)=
(3)3.5÷11

3

+6.5×[12×(11

3

-0.3)-15%
(4)已知:a

2

=b

3

=c

4

=20092010,求3a+b-2c

c-b+a

的值.
(5)1

1+2

+1

1+2+3

+1

1+2+3+4

+…+1

1+2+3+4+…+10

参考答案

(1)112+216+3112+…+101110,
=(1+2+3+…+10)+(12+16+112+…+1110),
=(1+10)×10÷2+(1-12+12-13+13-14+…+110-111),
=55+(1-111),
=55+1011,
=551011;

(2)(157×712+63412+14)÷(1-111),
=(127×712+27434)÷(1-111),
=(1+9)÷1011,
=10×1110,
=11;

(3)3.5÷113+6.5×[12×(113-0.3)-15%],
=72×34+132×[12×(113-310)-320],
=218+132×[12×3130-320],
=218+132×[625-320],
=218+132×494,
=218+6378,
=82.25;

(4)设200820092010=k,则a=2k,b=3k,c=4k,
则3a+b-2cc-b+a,
=3×2k+3k-2×4k4k-3k+2k,
=k3k,
=13;

(5)11+2+11+2+3+11+2+3+4+…+11+2+3+4+…+10,
=13+16+110+…+155,
=2×(12×3+13×4+…+110×11),
=2×(12-13+13-14+…110-111),
=2×(12-111),
=2×922,
=911.

考点:过程