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o.9就循环=1吗?1/7=0.142857循环2/7=0.285714循环1/7x2=2/70.142857循环x2=0.285714循环1/7x7=7/7=10.142857循环x7=0.9九循环
题目详情
o.9就循环=1吗?
1/7=0.142857循环
2/7=0.285714循环
1/7x2=2/7
0.142857循环x2=0.285714循环
1/7x7=7/7=1
0.142857循环x7=0.9九循环
1/7=0.142857循环
2/7=0.285714循环
1/7x2=2/7
0.142857循环x2=0.285714循环
1/7x7=7/7=1
0.142857循环x7=0.9九循环
▼优质解答
答案和解析
0.9的循环=1
证明如下：
0.9的循环=0.9+0.09+0.009+...
而0.9,0.09,0.009...为等比数列,公比为0.1
an=a1*q^(n-1)=0.9*0.1^(n-1)
令sn=0.9+0.09+0.009+...+0.9*0.1^(n-1)
lim(n→∞）sn=a1/(1-q)=0.9/(1-0.1)=0.9/0.9=1
∴得证.
证明如下：
0.9的循环=0.9+0.09+0.009+...
而0.9,0.09,0.009...为等比数列,公比为0.1
an=a1*q^(n-1)=0.9*0.1^(n-1)
令sn=0.9+0.09+0.009+...+0.9*0.1^(n-1)
lim(n→∞）sn=a1/(1-q)=0.9/(1-0.1)=0.9/0.9=1
∴得证.
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