5/2×3×4+7/3×4×5+.+17/8×9×10+19/9×10×11怎么求
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/27 05:12:33
5/2×3×4+7/3×4×5+.+17/8×9×10+19/9×10×11怎么求
2013某工大附中入学题
2013某工大附中入学题
![5/2×3×4+7/3×4×5+.+17/8×9×10+19/9×10×11怎么求](/uploads/image/z/6770049-33-9.jpg?t=5%2F2%C3%973%C3%974%2B7%2F3%C3%974%C3%975%2B.%2B17%2F8%C3%979%C3%9710%2B19%2F9%C3%9710%C3%9711%E6%80%8E%E4%B9%88%E6%B1%82)
∵5/(2×3×4)=(1/4)(1/2+1/3)=(1/2)(1/2-1/4)+1/3-1/4,
7/(3×4×5)=(1/5)(1/3+1/4)=(1/2)(1/3-1/5)+1/4-1/5,
9/(4×5×6)=(1/6)(1/4+1/5)=(1/2)(1/4-1/6)+1/5-1/6,
11/(5×6×7)=(1/7)(1/5+1/6)=(1/2)(1/5-1/7)+1/6-1/7,
13/(6×7×8)=(1/8)(1/6+1/7)=(1/2)(1/6-1/7)+1/7-1/8,
15/(7×8×9)=(1/9)(1/7+1/8)=(1/2)(1/7-1/9)+1/8-1/9,
17/(8×9×10)=(1/10)(1/8+1/9)=(1/2)(1/8-1/10)+1/9-1/10,
19/(9×10×11)=(1/11)(1/9+1/10)=(1/2)(1/9-1/11)+1/10-1/11.
∴将上述8个等式左右分别相加,得:
5/(2×3×4)+7/(3×4×5)+9/(4×5×6)+······+19/(9×10×11)
=(1/2)(1/2+1/3-1/10-1/11)+1/3-1/11
=1/4+(1/3)(1/2+1)-1/10-(1/11)(1/2+1)
=1/4+1/2-1/10-3/22
=3/4-1/10-3/22
=(1/2)(3/2-1/5-3/11)
=(1/2)[(15-2)/(2×5)-3/11]
=(1/2)(13/10-3/11)
=(1/2)(143-30)/110
=113/220.
再问: 可以简便运算吗?有点看不懂
再答: 这就是简便运算了
7/(3×4×5)=(1/5)(1/3+1/4)=(1/2)(1/3-1/5)+1/4-1/5,
9/(4×5×6)=(1/6)(1/4+1/5)=(1/2)(1/4-1/6)+1/5-1/6,
11/(5×6×7)=(1/7)(1/5+1/6)=(1/2)(1/5-1/7)+1/6-1/7,
13/(6×7×8)=(1/8)(1/6+1/7)=(1/2)(1/6-1/7)+1/7-1/8,
15/(7×8×9)=(1/9)(1/7+1/8)=(1/2)(1/7-1/9)+1/8-1/9,
17/(8×9×10)=(1/10)(1/8+1/9)=(1/2)(1/8-1/10)+1/9-1/10,
19/(9×10×11)=(1/11)(1/9+1/10)=(1/2)(1/9-1/11)+1/10-1/11.
∴将上述8个等式左右分别相加,得:
5/(2×3×4)+7/(3×4×5)+9/(4×5×6)+······+19/(9×10×11)
=(1/2)(1/2+1/3-1/10-1/11)+1/3-1/11
=1/4+(1/3)(1/2+1)-1/10-(1/11)(1/2+1)
=1/4+1/2-1/10-3/22
=3/4-1/10-3/22
=(1/2)(3/2-1/5-3/11)
=(1/2)[(15-2)/(2×5)-3/11]
=(1/2)(13/10-3/11)
=(1/2)(143-30)/110
=113/220.
再问: 可以简便运算吗?有点看不懂
再答: 这就是简便运算了
5/2×3×4+7/3×4×5+.+17/8×9×10+19/9×10×11怎么求
62比26怎么求比值 3.5比2.5怎么求比值 1.2米比4分米怎么求比值 3分之2比6怎么求比值 0.8比9分之5怎么
1 2 3 4 5 6 7 8 9 10 .这种三角的第10项的和怎么求?
1 2 3 4 5 6 7 8 9怎么=126求大神帮助
1 2 3 4 5 6 7 8 9 的中位数,众数和平均数怎么求?
行列式[2 1 -5 8 1 -3 0 9 0 2 -1 -5 1 4 -7 0] 怎么求
10除9除8除7除6除5除4除3除2 添小括号,求最小的结果,怎么添?
已知tanA=2,求4sinA-2cosA/5sinA+3cosA怎么求?
在Matlab里画折线图,横坐标为1,2,3,6,7,8,9,10,11,18,19,求问怎么写X=?
5,3,7/3,2,9/5,3/5,()这道题怎么解?求解题思路.
3,5,7的最小公倍数怎么求
-1+3-5+7-9+11-...+2011-2013+2015怎么算求详细解答