2*3/5*9+3*5/9*13+4*7/13*17+5*9/17*21+……+24*47/93*97+25*49/97*101裂项相
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通项为:(n+1)(n+2)/(4n+1)(4n+5)
咨询记录 · 回答于2022-07-05
2*3/5*9+3*5/9*13+4*7/13*17+5*9/17*21+……+24*47/93*97+25*49/97*101裂项相
通项为:(n+1)(n+2)/(4n+1)(4n+5)
通项为液败:(n+1)(2n+1)/(4n+1)(4n+5)设该项裂项为:A/(4n+1)-A/(4n+5)+B=(4A+16Bn^2+24Bn+5B)/(4n+1)(4n+5)故,4A+16Bn^2+6Bn+5B=(n+1)(2n+1)16Bn^2+24Bn+5B+4A=2n^2+3n+1有:16B=224B=35B+4A=1解伏毕得闹厅颤:A=3/32, B=1/8
故通项裂项为:(n+1)(2n+1)/(4n+1)(4n+5)=3/32*[1/(4n+1)-1/(4n+5)]+1/8
对于2*3/5*9+3*5/9*13+4*7/13*17+5*9/17*21+…羡银…兄败宴+24*47/93*97+25*49/97*101,n=24,原枯友式=24*1/8+3/32*(1/5-1/9+1/9-1/13+...+1/97-1/101)=3+3/32*(1/5-1/101)=3+3/32*96/505=3+9/505=1524/505
还没解答出来吗
而且显示已读,1524/505就是最后的结果。
通项为液败:(n+1)(2n+1)/(4n+1)(4n+5)设该项裂项为:A/(4n+1)-A/(4n+5)+B=(4A+16Bn^2+24Bn+5B)/(4n+1)(4n+5)故,4A+16Bn^2+6Bn+5B=(n+1)(2n+1)16Bn^2+24Bn+5B+4A=2n^2+3n+1有:16B=224B=35B+4A=1解伏毕得闹厅颤:A=3/32, B=1/8
故通项裂项为:(n+1)(2n+1)/(4n+1)(4n+5)=3/32*[1/(4n+1)-1/(4n+5)]+1/8
对于2*3/5*9+3*5/9*13+4*7/13*17+5*9/17*21+…羡银…兄败宴+24*47/93*97+25*49/97*101,n=24,原枯友式=24*1/8+3/32*(1/5-1/9+1/9-1/13+...+1/97-1/101)=3+3/32*(1/5-1/101)=3+3/32*96/505=3+9/505=1524/505