用数学归纳法证明:1-1/2+1/3-1/4+...+1/2n-1-1/2n=1/n+1+1/n+2+...+1/2n明天交,尽快,
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![用数学归纳法证明:1-1/2+1/3-1/4+...+1/2n-1-1/2n=1/n+1+1/n+2+...+1/2n明天交,尽快,](/uploads/image/z/941215-31-5.jpg?t=%E7%94%A8%E6%95%B0%E5%AD%A6%E5%BD%92%E7%BA%B3%E6%B3%95%E8%AF%81%E6%98%8E%3A1-1%2F2%2B1%2F3-1%2F4%2B...%2B1%2F2n-1-1%2F2n%3D1%2Fn%2B1%2B1%2Fn%2B2%2B...%2B1%2F2n%E6%98%8E%E5%A4%A9%E4%BA%A4%2C%E5%B0%BD%E5%BF%AB%2C)
用数学归纳法证明:1-1/2+1/3-1/4+...+1/2n-1-1/2n=1/n+1+1/n+2+...+1/2n明天交,尽快,
用数学归纳法证明:1-1/2+1/3-1/4+...+1/2n-1-1/2n=1/n+1+1/n+2+...+1/2n
明天交,尽快,
用数学归纳法证明:1-1/2+1/3-1/4+...+1/2n-1-1/2n=1/n+1+1/n+2+...+1/2n明天交,尽快,
1,n=1时,左边=1-1/2=1/2.右边=1/2成立
2,设n=k时成立就是 1-1/2+1/3-1/4+...+1/(2k-1)-1/2k=1/(k+1)+...1/(2k)
当 n=k+1时,则1-1/2+1/3+...+1/(2k-1)-1/2k+1/(2k+1)-1/(2k+2)=1/(k+1)+...1/(2k)+1/(2k+1)-1/(2k+2)=1/(k+2)+...+1/(2k)+1/(2k+1)+1/(k+1)-1/(2k+2)
下面证明 1/(k+1)-1/(2k+2)=1/(2k+2)?
1/(k+1)-1/(2k+2)=(2-1)/(2k+2)=1/(2k+2) !
所以 1-1/2+1/3+...+1/(2k-1)-1/2k+1/(2k+1)-1/(2k+2) = 1/(k+1)+...1/(2k)+ 1/(2k+1)+1/(2k+2)就是说 n=k+1时成立所以对于一切n都会成立
n=1自己证明
假设n=k成立,即:1-1/2+1/3-1/4+...+1/2k-1-1/2k=1/k+1+1/k+2+...+1/2k
则,当n=k+1时:
1-1/2+1/3-1/4+...+1/2k+1-1/2k+2=1/k+1+1/k+2+...+1/2k+1/2k+1-1/2k+2