Monday, April 29, 2019

sequences and series - Evaluate sumin=1nftyfrac1n(n+2)(n+4)?


How can I evaluate this?


n=11n(n+2)(n+4)=1135+1246+1357+1468+


I have tried:


1135+1357+1246+1468+=135(1+17)+146(12+18)+


and so on... Been stuck for a while. Result should be 1196



Answer



With *partial fractions:1k(k+2)(k+4)=18(1k2k+2+1k+4), we get a telescoping sum which simplifies to: 18(1+1213141n+11n+2+1n+3+1n+4).


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