【急】已知数列an满足1/a1a2+1/a2a3+……1/an-1an=(n-1)/a1an,求证为等差数列
问题描述:
【急】已知数列an满足1/a1a2+1/a2a3+……1/an-1an=(n-1)/a1an,求证为等差数列
已知数列an满足1/(a1a2)+1/(a2a3)+……1/(an-1an)=(n-1)/a1an,求证为等差数列.
答
n=3时1/a1a2 + 1/a2a3= 2/a1a3两边乘以 a1a2a3得到 a3+a1=2a2 前三项满足等差数列当n>=3时1/a1a2+1/a2a3+……1/an-1an=(n-1)/a1an ①1/a1a2+1/a2a3+……1/an-2an-1=(n-2)/a1an-1 ②①-②--->(n-1)/a1an-(n-2)/a1...