(1+3+5+7……+99+101)-(2+4+6……+98+100)1/(2*4)+1/(3*5)+1/(4*6).+1/(8*10)+1/(9*11)1 1 1 1 1 1___+___+___+___.....___+ ___ 第二题2*4 3*5 4*6 5*7 8*10 9*11
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(1+3+5+7……+99+101)-(2+4+6……+98+100)1/(2*4)+1/(3*5)+1/(4*6).+1/(8*10)+1/(9*11)1 1 1 1 1 1___+___+___+___.....___+ ___ 第二题2*4 3*5 4*6 5*7 8*10 9*11
(1+3+5+7……+99+101)-(2+4+6……+98+100)
1/(2*4)+1/(3*5)+1/(4*6).+1/(8*10)+1/(9*11)
1 1 1 1 1 1
___+___+___+___.....___+ ___ 第二题
2*4 3*5 4*6 5*7 8*10 9*11
(1+3+5+7……+99+101)-(2+4+6……+98+100)1/(2*4)+1/(3*5)+1/(4*6).+1/(8*10)+1/(9*11)1 1 1 1 1 1___+___+___+___.....___+ ___ 第二题2*4 3*5 4*6 5*7 8*10 9*11
(1+3+5+7……+99+101)-(2+4+6……+98+100)
=1+(3-2)+(5-4)+----+(101-100)
=1+1+1+---+1
=51
1/(2*4)+1/(3*5)+1/(4*6).+1/(8*10)+1/(9*11)
=(1/2)*(1/2-1/4+1/3-1/5+1/4-1/6+------+1/8-1/10+1/9-1/11)
=(1/2)*( 1/2+1/3-1/10-1/11)
=(1/2)*(5/6-21/110)
=53/165
第一问,(1+3+5+7……+99+101)—(1+3+5+7……+99)-100=1
=1+(3-2)+(5-4)+……(101-100)
=1+50*1
=51
=1/2-1/4+1/3-1/5+1/4-1/6……+1/8-1/10+1/9-1/11
=1/2+1/3-1/10-1/11
=232/330
=116/165
没有学过数列那就不跟你讲数列公式了。
(1+3+5+7……+99+101)-(2+4+6……+98+100)
=(1+3+5+7……+99)-(2+4+6……+98+100)+101【吧101拿出来是为了让前面两大项数量相等】
=(1-2)+(3-4)+(5-6)+……+(99-100)+101
=(-1)*50+101
=51
因为:
1/...
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没有学过数列那就不跟你讲数列公式了。
(1+3+5+7……+99+101)-(2+4+6……+98+100)
=(1+3+5+7……+99)-(2+4+6……+98+100)+101【吧101拿出来是为了让前面两大项数量相等】
=(1-2)+(3-4)+(5-6)+……+(99-100)+101
=(-1)*50+101
=51
因为:
1/(2*4)=(1/2)*[(1/2)-(1/4)]
1/(3*5)=(1/2)*[(1/3)-(1/5)]
所以:
1/(2*4)+1/(3*5)+1/(4*6)......+1/(8*10)+1/(9*11)
=(1/2)*【[(1/2)-(1/4)]+[(1/3)-(1/5)]+……+[(1/9)-(1/11)]】
=(1/2)*(1/2+1/3-1/10-1/11)
=53/165
收起
1 原式=(1+101)*((101-1)/2+1)-(2+100)*((100-2)/2+1)
=101*51-102*50
=51
2 原式=1/2*(1/2-1/4+1/3-1/5+。。。。+1/8-1/10+1/9-1/11)
=1/2*(1/2+1/3-1/10-1/11)
=53165
第二题的简便运算,是小学奥数中的,需要学习练习