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1/k(k+1)(k+2)数列题型比如1/k(k+1)可以拆成1/k-1/(k+1)然后再用叠加法求an,那1/k(k+1)(k+2)也要拆成两数相减的形式,怎么拆,

题目详情
1/k(k+1)(k+2) 数列题型
比如1/k(k+1)可以拆成 1/k - 1/(k+1) 然后再用叠加法求an,那1/k(k+1)(k+2)也要拆成两数相减的形式,怎么拆,
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答案和解析
1/k(k+1)(k+2)=[(k+1)-k]/k(k+1)(k+2)=1/k(k+2)-1/(k+1)(k+2)=(1/2)[(k+2)-k)]/k(k+2)-[(k+2)-(k+1)]/(k+1)(k+2)=(1/2)[1/k-1/(k+2)]-1/(k+1)+1/(k+2)=(1/2)(1/k)+(1/2)[1/(k+2)]-1/(k+1)=(1/2)[1/k+1/(k+2)]-1/(k+1...