求数学题怎么做
2018-03-29
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第n项的分母为n(n+2),
第n项为=1/n(n+2)=(1/2)(1/n-1/(n+2))
那么,前n项的和为
(1/2)(1/1-1/3+1/2-1/4+1/3-1/5+......+1/n-1/(n+2))
=(1/2)(1+1/2-1/(n+1)-1/(n+2))
=(1/2)(3/2-(2n+3)/((n+1)(n+2)))
=(3n²+9n+6-(4n+6))/(4(n+1)(n+2))
=(3n²+5n)/(4(n+1)(n+2))
第n项为=1/n(n+2)=(1/2)(1/n-1/(n+2))
那么,前n项的和为
(1/2)(1/1-1/3+1/2-1/4+1/3-1/5+......+1/n-1/(n+2))
=(1/2)(1+1/2-1/(n+1)-1/(n+2))
=(1/2)(3/2-(2n+3)/((n+1)(n+2)))
=(3n²+9n+6-(4n+6))/(4(n+1)(n+2))
=(3n²+5n)/(4(n+1)(n+2))
更多追问追答
追问
代值之后不对
追答
我带入n=1,2答案都是对的。
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