初一数学题1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+......+1/(1+2+3+...+100)快的好的50悬赏

这道题我看不懂,请给出过程并讲解。快的好的50悬赏

因为:
1/(1+2)=1/3=2*(1/2-1/3)
1/(1+2+3)=1/6=2*(1/3-1/4)
1/(1+2+3+4)=1/10=2*(1/4-1/5)
............同理
1/(1+2+3+...+100)=1/5050=2*(1/100-1/101)
所以
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+......+1/(1+2+3+...+100)
=1+2*【(1/2-1/3)+(1/3-1/4)+(1/4-1/5).......+(1/100-1/101)】
=1+2*【1/2-1/101】去掉小括号,中间部分相加为0,只剩下头尾
=1+2*99/202
=1+99/101
=200/101追问

还有道英语题。别介意哈。there are ____vegetable and____ fruit in the fridge
a.too much ,too many b.too many ,too much c.much too,many too d.too many,much too

追答

选A.

解释:fruit 和vegetable既可以作可数名词又可以作不可数名词。
fruit作水果解释的时候,既是可数名词,又是不可数名词。作果实解释的时候是可数名词。但在中文里的确不好分辩。具体叙述是不可数,如果指好几种不同类的水果可以用复数。例如:
The potato is a vegetable, not a fruit. 土豆是蔬菜,不是水果。
The drink is made from four tropical fruits. 这种饮料是四种热带水果做成的。
当vegetable表示的是所有蔬菜时是可数,如:
I like vegetables.
如果是表示的是一个数时就不可数,如:
I have a lot of vegetable.
too much 和too many都表示很多的意思,修饰名词。
其中,too much 修饰不可数名词,too many 修饰可数名词。
much too 只用作副词作状语,但它不单独使用,在句子中要修饰形容词或副词,但不修饰动词。如:
You are much too kind to me.你对我实在太好了。
It's much too cold.天气实在太冷了。
根据there be结构的就近原则,此处是are,说明后面的蔬菜是作可数名词.所以第一空填too many,用排除法,选B

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第1个回答  2013-11-09
解:原式Sn=1+1/3+1/6+……+2/[(1+n)·n]+……+1/5050 (因为分母是等差数列前n项和,2/[(1+n)·n]是通项) 令An=2/[(1+n)n] =2[1/n-1/(1+n)]
∴Sn=A1+A2+A3+...+An
=2[1-1/2+1/2-1/3+...+1/n-1/(1+n)]
=2[(1-1/(1+n)]
带入值得Sn=200/101

初中应该还没学等差数列……所以应该不适合,可以参考下。追问

还有道英语题。别介意哈。there are ____vegetable and____ fruit in the fridge
a.too much ,too many b.too many ,too much c.much too,many too d.too many,much too

追答

c

追问

much too是神马意思呢?不要百度搜的大长篇

追答

too much 太多,much too ,多

追问

可fruit没+s

追答

你还是自己看下吧,我也不清楚了

第2个回答  2013-11-09
1+2=2*3/2
1+2+3=3*4/2
1+2+3+4=4*5/2
.........
1+2+3+……+100=100*101/2
所以,
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+100)
=1+2/(2*3)+2/(3*4)+2/(4*5)+……+2/(100*101)
=2[(1/2+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(100*101)〕
因为:
1/(2*3)=1/2-1/3;
1/(3*4)=1/3-1/4;
1/(4*5)=1/4-1/5;
……
1/(100*101)=1/100-1/101
所以,
原式=2(1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/100-1/101)
=2(1-1/101)
=2*100/101
=200/101追问

还有道英语题。别介意哈。there are ____vegetable and____ fruit in the fridge
a.too much ,too many b.too many ,too much c.much too,many too d.too many,much too

追答

你蔬菜后面没S?
题打的就不对

追问

没s

第3个回答  2013-11-09
1/(1+2)=1/[(1+2)*2/2]=2/[(1+2)*2]=2/(3*2)
1/(1+2+3)=1/[(1+3)*3/2]=2/[(1+3)*3]=2/(4*3)
1/(1+2+3+4)=1/[(1+4)*4/2]=2/[(1+4)*4]=2/(5*4)
1/(1+2+3+4+5)=1/[(1+5)*5/2]=2/[(1+5)*5]=2/(6*5)
……
1/(1+2+3+4+5……+100)=1/[(1+100)*100/2]=2/[(1+100)*100]=2/(101*100)

原式=1+2/(3*2)+2/(4*3)+2/(5*4)+……2/(101*100)
=1+2*[1/(3*2)+1/(4*3)+1/(5*4)+……1/(101*100)]
=1+2*[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)……+(1/100-1/101)]
=1+2*[1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……1/100-1/101]
=1+2*[1/2-1/101]
=1+1-2/101
=200/101追问

还有道英语题。别介意哈。there are ____vegetable and____ fruit in the fridge
a.too much ,too many b.too many ,too much c.much too,many too d.too many,much too

追答

我觉得是b,vegetable后面有s吗

追问

没s

追答

too many+可数名词复数‘太多’
many too(没有这种用法)
too much +不可数名词‘太多’
much too +形容词‘太……

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