题目
三道数学题,快呀
11+12-13-14+15+16-17-18+……+99+100(要过程)
1+(-2)+3+(-4)+5+(-6)+……+2007+(-2008)(过程)
1-2+3-4+5-6+……-100+101
n(n+2)分之1=
11+12-13-14+15+16-17-18+……+99+100(要过程)
1+(-2)+3+(-4)+5+(-6)+……+2007+(-2008)(过程)
1-2+3-4+5-6+……-100+101
n(n+2)分之1=
提问时间:2020-12-20
答案
1、11+12-13-14+15+16-17-18+…+99+100
=11+12+(-13-14+15+16)+(-17-18+19+20)+…+(-97-98+99+100)
=23+(4+4+……+4)
=23+4*22
=111.
2、1+3+5+……+2007+(-2)+(-4)+……(-2008)
= 1004*1+(1004*1003)+1004*(-2)+1004*1003
=-1004
3、1-2+3-4+5-6+…-100+101=(1-2)+(3-4)+...+(99-100)+101=(-1)x50+101= 51
4、1/(n(n+1)(n+2)
=(1/2)*2/n(n+1)(n+2)
=(1/2)*[(n+2)-n]/n(n+1)(n+2)
=(1/2)*[(n+2)/n(n+1)(n+2)-n/n(n+1)(n+2)]
=(1/2)*[1/n(n+1)-1/(n+1)(n+2)]
所以1/1*2*3+……+1/n(n+1)(n+2)
=(1/2)*[1/1*2-1/2*3+……+1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*[1/1*2-1/(n+1)(n+2)]
=(n²+3n)/(4n²+12n+8)
=11+12+(-13-14+15+16)+(-17-18+19+20)+…+(-97-98+99+100)
=23+(4+4+……+4)
=23+4*22
=111.
2、1+3+5+……+2007+(-2)+(-4)+……(-2008)
= 1004*1+(1004*1003)+1004*(-2)+1004*1003
=-1004
3、1-2+3-4+5-6+…-100+101=(1-2)+(3-4)+...+(99-100)+101=(-1)x50+101= 51
4、1/(n(n+1)(n+2)
=(1/2)*2/n(n+1)(n+2)
=(1/2)*[(n+2)-n]/n(n+1)(n+2)
=(1/2)*[(n+2)/n(n+1)(n+2)-n/n(n+1)(n+2)]
=(1/2)*[1/n(n+1)-1/(n+1)(n+2)]
所以1/1*2*3+……+1/n(n+1)(n+2)
=(1/2)*[1/1*2-1/2*3+……+1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*[1/1*2-1/(n+1)(n+2)]
=(n²+3n)/(4n²+12n+8)
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