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观察下列各式:12+1−112+1=1−112+1=1−(1−12),22+2−122+2=1−122+2=1−(12−13),32+3−132+3=1−132+3=1−(13−14),…计算:12+522+2+1132+3+…+20112+2011−120112+2011=201012012201012012.

题目详情

12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),


计算:
1
2
+
5
22+2
+
11
32+3
+…+
20112+2011−1
20112+2011
=
2010
1
2012
2010
1
2012
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
12+1−1
12+1
=1−
1
12+1
=1−(1−
1
2
),
12+1−1
12+1
12+1−112+1−112+1−112+1−12+1−112+112+112+112+12+1
1
12+1
1112+112+112+112+12+1
1
2
1122
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
22+2−1
22+2
=1−
1
22+2
=1−(
1
2
1
3
),
22+2−1
22+2
22+2−122+2−122+2−122+2−12+2−122+222+222+222+22+2
1
22+2
1122+222+222+222+22+2
1
2
1122
1
3
1133
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
32+3−1
32+3
=1−
1
32+3
=1−(
1
3
1
4
),
32+3−1
32+3
32+3−132+3−132+3−132+3−12+3−132+332+332+332+32+3
1
32+3
1132+332+332+332+32+3
1
3
1133
1
4
1144

1
2
+
5
22+2
+
11
32+3
+…+
20112+2011−1
20112+2011
=
2010
1
2012
2010
1
2012
1
2
1122
5
22+2
5522+222+222+222+22+2
11
32+3
111132+332+332+332+32+3
20112+2011−1
20112+2011
20112+2011−120112+2011−120112+2011−120112+2011−12+2011−120112+201120112+201120112+201120112+20112+2011
2010
1
2012
1
2012
1
2012
1120122012
2010
1
2012
1
2012
1
2012
1120122012
▼优质解答
答案和解析
根据题意,12+522+2+1132+3+…+20112+2011−120112+2011=1-(1-12)+1-(12-13)+1-(13-14)+…+1-(12011-12012)=1×2011-1+12-12+13-13+14-…-12011+12012=2011-1+12012=201012012.故答案为:201012012....