作业帮计算1/1*4+1/4*7+1/7*10+1/10*13+1/13*16的答案过程
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计算1/1*4+1/4*7+1/7*10+1/10*13+1/13*16的答案过程
计算1/1*4+1/4*7+1/7*10+1/10*13+1/13*16的答案过程
计算1/1*4+1/4*7+1/7*10+1/10*13+1/13*16的答案过程
1/1*4+1/4*7+1/7*10+1/10*13+1/13*16
=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+1/3*(1/10-1/13)+1/3*(1/13-1/16)
=1/3*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3*(1-1/16)
=1/3*15/16
=5/16
根据裂项公式 （b-a）/ab=1/a-1/b
得 原式=1/3（3/1*4+3/4*7+3/7*10+3/10*13+3/13*16）
=1/3（1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16）
=1/3（1-1/16）
=1/3*15/16
=5/16
1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)+1/(13*16)
=1/3*[(4-1)/(1*4)+(7-4)/(4*7)+(10-7)/(7*10)+(13-10)/(10*13)+(16-13)/(13*16)]
=1/3*[1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16]
=1/3*[1-1/16]
=1/3*15/16
=5/16
*1/1*4+1/4*7+1/7*10+1/10*13+1/13*16
=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+1/3*(1/10-1/13)+1/3*(1/13-1/16)
=1/3*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3*(1-1/16)
=1/3*15/16
=5/16
*是×号