已知数列{an}满足:a1=1,且an-a(n-1)=2n.求a2,a3,a4.求数列{an}通项an
问题描述:
已知数列{an}满足:a1=1,且an-a(n-1)=2n.求a2,a3,a4.求数列{an}通项an
答
a2-a1=2*2=4a2=4+1=5a3-a2=2*3=6a3=6+5=11a4-a3=2*4=8a4=11+8=192、an-a(n-1)=2na(n-1)-a(n-2)=2(n-1)……a3-a2=2*3a2-a1=2*2相加,中间正负抵消an-a1=2*2+2*3+……+2n=2(2+3+……+n)=2*(n+2)(n-1)/2=n²+n-2a1=1...