一定得有过程哈,谢谢(wyhhh1986 初入江湖 二级,括号中的和为1呀?我觉得不对也.)
三分之一加五分之三再加七分之五,一直加到一千零一分之九百九十九
=(1-2/3)+(1-2/5)+(1-2/7)+……+(1-2/1001)
=500-(2/3+2/5+2/7+……+2/1001)
=500-2×(1/3+1/5+1/7+……+1/1001)
至此确实没有简便办法:
但是我们知道:
1+1/2+1/3+……+1/(2n+1)为调和数级 他的近似值:
1+1/2+1/3+……+1/(2n+1)=ln(2n+1)+0.5772157....(1)
1+1/2+1/3+……+1/n=lnn+0.5772157 变形,两边同时除2
1/2+1/4+……+1/2n=1/2*lnn+0.5772157/2...(2)
(1)-(2)得
1+1/3+……+1/(2n+1)=ln(2n+1)-1/2*lnn+0.5772157/2
所以:1/3+……+1/(2n+1)=ln(2n+1)-1/2*lnn-0.71138215
1/(2n+1)=1/1001时,x=500
把x=500代入上式 :
1/3+1/5+...+1/1001=ln1001-(1/2)*ln1000-0.71138215
ln1001约为6.908755 ln500约为6.2146
1/3+1/5+...+1/1001=3.09
所以原式=500-2×(1/3+1/5+1/7+……+1/1001)
≈500-6.18=493.82
=(1-2/3)+(1-2/5)+(1-2/7)+……+(1-2/1001)
=500-(2/3+2/5+2/7+……+2/1001)
=500-2×(1/3+1/5+1/7+……+1/1001)
至此确实没有简便办法:
但是我们知道:
1+1/2+1/3+……+1/(2n+1)为调和数级 他的近似值:
1+1/2+1/3+……+1/(2n+1)=ln(2n+1)+0.5772157....(1)
1+1/2+1/3+……+1/n=lnn+0.5772157 变形,两边同时除2
1/2+1/4+……+1/2n=1/2*lnn+0.5772157/2...(2)
(1)-(2)得
1+1/3+……+1/(2n+1)=ln(2n+1)-1/2*lnn+0.5772157/2
所以:1/3+……+1/(2n+1)=ln(2n+1)-1/2*lnn-0.71138215
1/(2n+1)=1/1001时,x=500
把x=500代入上式 :
1/3+1/5+...+1/1001=ln1001-(1/2)*ln1000-0.71138215
ln1001约为6.908755 ln500约为6.2146
1/3+1/5+...+1/1001=3.09
所以原式=500-2×(1/3+1/5+1/7+……+1/1001)
≈500-6.18=493.82
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第1个回答 2008-09-26
=(1-2/3)+(1-2/5)+(1-2/7)+……+(1-2/1001)
=500-(2/3+2/5+2/7+……+2/1001)
=500-2×(1/3+1/5+1/7+……+1/1001)
这个是没有简便方法可做的
后面这个1/3+1/5+1/7+……+1/1001是调和数级 只能求他的近似值
1/3+1/5+1/7+……+1/1001=ln1001+c
c是欧拉常数 约等于0.577
ln1001约为6.9
那么原式=500-2×(ln1001+c)≈486
答案约为486
=500-(2/3+2/5+2/7+……+2/1001)
=500-2×(1/3+1/5+1/7+……+1/1001)
这个是没有简便方法可做的
后面这个1/3+1/5+1/7+……+1/1001是调和数级 只能求他的近似值
1/3+1/5+1/7+……+1/1001=ln1001+c
c是欧拉常数 约等于0.577
ln1001约为6.9
那么原式=500-2×(ln1001+c)≈486
答案约为486
参考资料:仅供参考,祝您学习进步!
第2个回答 2008-09-26
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161090552989977494023692552287036801190213650067362710849346814285569500567645
906662554620702838957102937933543406839318254368565643249729318273170027202685
471170651498435490449678390370060649010446440327282511547624279047107098901820
421326765490887514129734596355326319332516606039670643459924370306310732302460
420282591506781264610503566296276693579388/126577863541638726086050855037540357256185349110189862223934694445211720305062
349067408454401879822210790444194239617480699223438700657124493357084593485992
057639704247162581853246852733259736216353257003773503901727609430853604086083
752774020308842526079709913311592009579914617325187465364461572049536991348575
936350284844879936987518365255944278175619290722401953513637701939806853616336
2381397212249803211556760067107764844375
这是一个分子和分母都很大的分数,约等于493.8198837068918327797,惭愧,没发现简便方法。
161090552989977494023692552287036801190213650067362710849346814285569500567645
906662554620702838957102937933543406839318254368565643249729318273170027202685
471170651498435490449678390370060649010446440327282511547624279047107098901820
421326765490887514129734596355326319332516606039670643459924370306310732302460
420282591506781264610503566296276693579388/126577863541638726086050855037540357256185349110189862223934694445211720305062
349067408454401879822210790444194239617480699223438700657124493357084593485992
057639704247162581853246852733259736216353257003773503901727609430853604086083
752774020308842526079709913311592009579914617325187465364461572049536991348575
936350284844879936987518365255944278175619290722401953513637701939806853616336
2381397212249803211556760067107764844375
这是一个分子和分母都很大的分数,约等于493.8198837068918327797,惭愧,没发现简便方法。
第3个回答 2008-09-25
解:1-2/3+1-2/5+....1-2/1001 有 (1001-3)/2 +1个1才对,即500个1
=500-2*(1/3+1/5+.....+1/1001)
哎,,失败,,括号里的不知道怎么算呢
=500-2*(1/3+1/5+.....+1/1001)
哎,,失败,,括号里的不知道怎么算呢
第4个回答 2008-09-25
997
1-2/3+1-2/5+....1-2/1001=999-2*(1/3+1/5+.....1/1001)=997
1-2/3+1-2/5+....1-2/1001=999-2*(1/3+1/5+.....1/1001)=997