1/(19*21)+1/(21*23)+1/(23*25)+1/(25*27)+.+1/(97*99)式子为什么要提取1/2?
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![1/(19*21)+1/(21*23)+1/(23*25)+1/(25*27)+.+1/(97*99)式子为什么要提取1/2?](/uploads/image/z/135451-19-1.jpg?t=1%2F%EF%BC%8819%2A21%EF%BC%89%2B1%2F%EF%BC%8821%2A23%EF%BC%89%2B1%2F%EF%BC%8823%2A25%EF%BC%89%2B1%2F%EF%BC%8825%2A27%EF%BC%89%2B.%2B1%2F%EF%BC%8897%2A99%EF%BC%89%E5%BC%8F%E5%AD%90%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%E6%8F%90%E5%8F%961%2F2%3F)
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1/(19*21)+1/(21*23)+1/(23*25)+1/(25*27)+.+1/(97*99)式子为什么要提取1/2?
1/(19*21)+1/(21*23)+1/(23*25)+1/(25*27)+.+1/(97*99)式子为什么要提取1/2?
1/(19*21)+1/(21*23)+1/(23*25)+1/(25*27)+.+1/(97*99)式子为什么要提取1/2?
因为每项分母相乘的两个数相差2,裂项后每项的数值是裂项前2倍,所以要乘以1/2
如1/(19*21)=(1/19-1/21)*(1/2)