帮忙解2道奥数题!简便运算,十分感谢,最好有个解释,急求!1. 1+(2+1)/1 + (1+2+3)/1 + (1+2+3+4)/1 + ...+ (1+2+3+4+L+100)/12. [1—(2×2)/1]×[1-(3×3)/1〕×[1-(4×4)/1]×L×[1-(100×100
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![帮忙解2道奥数题!简便运算,十分感谢,最好有个解释,急求!1. 1+(2+1)/1 + (1+2+3)/1 + (1+2+3+4)/1 + ...+ (1+2+3+4+L+100)/12. [1—(2×2)/1]×[1-(3×3)/1〕×[1-(4×4)/1]×L×[1-(100×100](/uploads/image/z/1251871-7-1.jpg?t=%E5%B8%AE%E5%BF%99%E8%A7%A32%E9%81%93%E5%A5%A5%E6%95%B0%E9%A2%98%21%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%2C%E5%8D%81%E5%88%86%E6%84%9F%E8%B0%A2%2C%E6%9C%80%E5%A5%BD%E6%9C%89%E4%B8%AA%E8%A7%A3%E9%87%8A%2C%E6%80%A5%E6%B1%82%211.++1%2B%282%2B1%29%2F1++%2B++++%281%2B2%2B3%EF%BC%89%2F1+++%2B++++%281%2B2%2B3%2B4%29%2F1+++%2B++...%2B++%281%2B2%2B3%2B4%2BL%2B100%EF%BC%89%2F12.+++%5B1%E2%80%94%EF%BC%882%C3%972%EF%BC%89%EF%BC%8F1%5D%C3%97%5B1%EF%BC%8D%EF%BC%883%C3%973%EF%BC%89%EF%BC%8F1%E3%80%95%C3%97%5B1%EF%BC%8D%EF%BC%884%C3%974%EF%BC%89%EF%BC%8F1%5D%C3%97L%C3%97%5B1%EF%BC%8D%EF%BC%88100%C3%97100)
帮忙解2道奥数题!简便运算,十分感谢,最好有个解释,急求!1. 1+(2+1)/1 + (1+2+3)/1 + (1+2+3+4)/1 + ...+ (1+2+3+4+L+100)/12. [1—(2×2)/1]×[1-(3×3)/1〕×[1-(4×4)/1]×L×[1-(100×100
帮忙解2道奥数题!简便运算,十分感谢,最好有个解释,急求!
1. 1+(2+1)/1 + (1+2+3)/1 + (1+2+3+4)/1 + ...+ (1+2+3+4+L+100)/1
2. [1—(2×2)/1]×[1-(3×3)/1〕×[1-(4×4)/1]×L×[1-(100×100)/1
第一题:一加上二加一分之一加上一加二加三分之一.以此类推.
第二题:一减二乘二分之一的差乘一减三成三的分之一的差.以此类推.
六年级的奥数题,帮帮忙!急求!
帮忙解2道奥数题!简便运算,十分感谢,最好有个解释,急求!1. 1+(2+1)/1 + (1+2+3)/1 + (1+2+3+4)/1 + ...+ (1+2+3+4+L+100)/12. [1—(2×2)/1]×[1-(3×3)/1〕×[1-(4×4)/1]×L×[1-(100×100
按你的意思应该写成1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
=1+1/3+1/6+1/10+...+1/n(n+1)/2 (1加上三分之一加上六分之一...)
=2*[1/2+1/6+1/12+1/20+...+1/n(n+1)] (每一项分母乘以2)
=2*[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1)] 拆分每一项如1/6=1/2-1/3
=2*[1-1/(n+1)]
=2*n/(n+1)代入n的值
=200/101
第二道题应该写为(1-1/4)*(1-1/9)*(1-1/14)*...*(1-1/100)
每一项其实可以看成以下两个数的乘积 :(n-1)除以n * (n+1)除以n
如1-1/4=1/2*3/2
原题
=1/2*3/2*2/3*4/3*3/4*5/4*...*(n-1)/1*(n+1)/n
=1/2*(n+1)/n
=(n+1)/2n
代入n的值
=101/200