计算1/2+1/6+1/12+1/20+.+1/9900=？这道数学题怎么做？大神们帮帮忙
计算1/2+1/6+1/12+1/20+.+1/9900=？这道数学题怎么做？大神们帮帮忙
1/2+1/6+1/12+1/20+......+1/9900 =1/2+1/2-1/3+1/3-1/4+....+1/99-1/100 =1-1/100 =99/100
麻烦采纳，谢谢!
1/2+1/6+1/12+1/20+.+1/132=？求大神帮助
1/2=1/(1*2)=1-1/2 1/6=1/(2*3)=1/2-1/3 1/12=1/(3*4)=1/3-1/4 1/20=1/(4*5)=1/4-1/5 1/30=1/(5*6)=1/5-1/6 1/42=1/(6*7)=1/6-1/7 注意1/(A*B)这样的式子.A和B相差1个数.A小与B就能化成 1/A-1/B的式子 则原式 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/11-1/12 =1-1/12 =11/12
1/2+1/6+1/12+1/20+.+1/4022030=?
1/2+1/6+1/12+1/20+......+1/4022030
=1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + ...+ 1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2005-1/2006
=1-1/2006
=2005/2006
1/2+1/6+1/12+1/20+.+1/110=?
解答：
1/2+1/6+1/12+1/20+........+1/110
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+........+1/(10*11)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/10-1/11
=1-1/11
=10/11
1/2+1/6+1/12+1/20+.+1/4026042?
1/2+1/6+1/12+1/20+1/30+......+1/4026042
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/2006-1/2007)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2006-1/2007
=1-1/2007
=2006/2007
帮忙想个题：简算：1/2+1/6+1/12+1/20+.+1/110=? 过程！谢谢！
1/1-1/2+1/2-1/3+1/3-1/4+.....+1/9-1/10+1/10-1/11=10/11
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 这道数学题的简便运算怎么解
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+.........+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+1/20+.+1/n(n+1)
这是中学的奥赛题啦，不是用电脑算的啦。
上题解答如下
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+(5-4)/4*5...+(n+1-n)/n*(n+1)
=2/1*2-1/1*2+3/2*3-2/2*3+4/3*4-3/3*4+5/4*5-4/4*5..+(n+1)/n(n+1)-n/n(n+1)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...+1/n-1/(n+1)
=1-1/(n+1)
1/2+1/6+1/12+1/20+.+1/78+1/90简便算法怎么做？
1/2+1/6+1/12+1/20+......+1/78+1/90
=1/1*2+1/2*3+1/3*4+……+1/9*10
=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10
=1-1/10
=9/10
