1/(1+2)+1/(2+3)+1/(3+4)+...+1/(99+100)=?

来源：百度知道编辑：UC知道时间：2024/06/15 15:55:44

=(1-1/2)+(1/2-1/3)+...+(1/99-1/100)
=1-1/100=99/100

结果等于一个分数:

分子为6019484180875094293775771025953918105702575294840191045657968324602140467851923044049097
分母为
2635106162757236442495826303084698495565581115509040892412867358728390766099042109898375
化成小数大约为2.28434

分子为6019484180875094293775771025953918105702575294840191045657968324602140467851923044049097
分母为
2635106162757236442495826303084698495565581115509040892412867358728390766099042109898375
化成小数大约为2.28434

1/3+1/6+1/12+...+1/199=1/3+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)...+(1/99-1/100)=1/3+1/2-1/3+1/3-1/4+1/4-1/5...+1/99-1/100=1/3+1/2-1/100=247/300

1/2-1/2=? 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1+1/1+2+1/1+2+3.........+1/1+2+3.....100 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2) 3/2=2+1/1*2=1/1+1/2 (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)