1/(1*3)+1/(3*5)+1/(5*7)+....1/(99*101)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+......(1/99-1/101)/2
=(1-1/3+1/3-1/5+1/5-1/7+......1/99-1/101)/2
=(1-1/101)/2
=(100/101)/2
=50/101
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é¾éæ¯ï¼1*1/3+3*1/5+5*1/7+......99*1/101
=1/3+3/5+5/7+......99/101
=(1-2/3)+(1-2/5)+(1-2/7)+......(1-2/101)
=(1+1+1...å ±50个1) - 2 * (1/3+1/5+1/7+......1/101)
=50-2(1/3+1/5+1/7+......1/101)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+......(1/99-1/101)/2
=(1-1/3+1/3-1/5+1/5-1/7+......1/99-1/101)/2
=(1-1/101)/2
=(100/101)/2
=50/101
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é¾éæ¯ï¼1*1/3+3*1/5+5*1/7+......99*1/101
=1/3+3/5+5/7+......99/101
=(1-2/3)+(1-2/5)+(1-2/7)+......(1-2/101)
=(1+1+1...å ±50个1) - 2 * (1/3+1/5+1/7+......1/101)
=50-2(1/3+1/5+1/7+......1/101)
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第1个回答 2011-01-24
你题目打错了吧？
应该是这样的题目：
1/(1*3)+1/(3*5)+1/(5*7)+…+1/(99*101)
解：
因为1/（1*3）=1/2*(1/1-1/3)
1/（3*5）=1/2*(1/3-1/5)
1/（5*7）=1/2*(1/5-1/7)
……
1/（99*101）=1/2*(1/99-1/101)
所以：
1/(1*3)+1/(3*5)+1/(5*7)+…+1/(99*101)
=1/2*(1/1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+…+1/2*(1/99-1/101)
=1/2*[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+…+(1/99-1/101)]
=1/2*(1/1-1/3+1/3-1/5+1/5-1/7+…+1/99-1/101)
=1/2*(1/1-1/101)
=1/2*(100/101)
=50/101
分解2=3-1=5-3=7-5=-=101-99
所以 1/1＊3+1/3＊5+1/5＊7+-+1/99＊101
=1/2(2/1＊3+2/3＊5++-+2/99＊101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=1/2(1-1/101)
=100/202
应该是这样的题目：
1/(1*3)+1/(3*5)+1/(5*7)+…+1/(99*101)
解：
因为1/（1*3）=1/2*(1/1-1/3)
1/（3*5）=1/2*(1/3-1/5)
1/（5*7）=1/2*(1/5-1/7)
……
1/（99*101）=1/2*(1/99-1/101)
所以：
1/(1*3)+1/(3*5)+1/(5*7)+…+1/(99*101)
=1/2*(1/1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+…+1/2*(1/99-1/101)
=1/2*[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+…+(1/99-1/101)]
=1/2*(1/1-1/3+1/3-1/5+1/5-1/7+…+1/99-1/101)
=1/2*(1/1-1/101)
=1/2*(100/101)
=50/101
分解2=3-1=5-3=7-5=-=101-99
所以 1/1＊3+1/3＊5+1/5＊7+-+1/99＊101
=1/2(2/1＊3+2/3＊5++-+2/99＊101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=1/2(1-1/101)
=100/202
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