几道简算题
计算:1.|1/3-1/2|+|1/4-1/3|+|1/5-1/4|……+|1/2006-1/2005|2.1/2*1,+1/(2+1)*(1+1),+1/(2+2)*(...
计算:1.|1/3-1/2|+|1/4-1/3|+|1/5-1/4|……+|1/2006-1/2005|
2.1/2*1,+1/(2+1)*(1+1),+1/(2+2)*(1*2),……(2+2009)*(1+2009)
3.1,+1/1+2,+1/1+2+3,……1/1+2+3……100
注:/为分数线,/前面的是分子,后面的是分母。后两题每个分数后面,都会有一个逗号来区分
第二题写错了,后面应该是1/(2+2009)*(1+2009) 展开
2.1/2*1,+1/(2+1)*(1+1),+1/(2+2)*(1*2),……(2+2009)*(1+2009)
3.1,+1/1+2,+1/1+2+3,……1/1+2+3……100
注:/为分数线,/前面的是分子,后面的是分母。后两题每个分数后面,都会有一个逗号来区分
第二题写错了,后面应该是1/(2+2009)*(1+2009) 展开
2个回答
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1.|1/3-1/2|+|1/4-1/3|+|1/5-1/4|……+|1/2006-1/2005|
=1/2-1/3+1/3-1/4+1/4-1/5+....+1/2005-1/2006
=1/2-1/2006
=1003/2006-1/2006
=1002/2006
=501/1003
2.1/2*1,+1/(2+1)*(1+1),+1/(2+2)*(1*2),……(2+2009)*(1+2009)
=1-1/2+1/2-1/3+1/3-1/4+.....+1/2010-1/2011
=1-1/2011
=2010/2011
3.1+1/1+2+1/1+2+3……1/1+2+3……100
=2/(1*2)+2/(2*3)+2/3*4+....+2/100*101
=2[1/1*2+1/2*3+1/3*4+...+1/100*101]
=2*(1-1/2+1/2-1/3+1/3-1/4……+1/100-1/101)
=2*(1-1/101)
=2*100/101
=50/101
=1/2-1/3+1/3-1/4+1/4-1/5+....+1/2005-1/2006
=1/2-1/2006
=1003/2006-1/2006
=1002/2006
=501/1003
2.1/2*1,+1/(2+1)*(1+1),+1/(2+2)*(1*2),……(2+2009)*(1+2009)
=1-1/2+1/2-1/3+1/3-1/4+.....+1/2010-1/2011
=1-1/2011
=2010/2011
3.1+1/1+2+1/1+2+3……1/1+2+3……100
=2/(1*2)+2/(2*3)+2/3*4+....+2/100*101
=2[1/1*2+1/2*3+1/3*4+...+1/100*101]
=2*(1-1/2+1/2-1/3+1/3-1/4……+1/100-1/101)
=2*(1-1/101)
=2*100/101
=50/101
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1、|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+......+|1/2006-1/2005|
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……(1/2005/-1/2006)
=1/2-1/3+1/3-1/4+1/4-1/5+……1/2005/-1/2006
=1/2-1/2006
=501/1003
2、
3、分母是等差数列求和原式=2(1/(1*2)+1/(2*3)+……+1/(100*101))(求和后的)=200/101
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……(1/2005/-1/2006)
=1/2-1/3+1/3-1/4+1/4-1/5+……1/2005/-1/2006
=1/2-1/2006
=501/1003
2、
3、分母是等差数列求和原式=2(1/(1*2)+1/(2*3)+……+1/(100*101))(求和后的)=200/101
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