数列
数列{An}满足A1=1,A2=2,A(N+2)=[1+cos^2(n∏/2)] An+sin^2(n∏/2),n=1,2,3…… (1)求A3,A4,并求数列{An}的通项公式 (2)设Bn=A(2n-2)/A2n,Sn=B1+B2+……+Bn,证明:当n≥6时,(Sn-2)的绝对值<1/n
数列{An}满足A1=1,A2=2,A(n+2)=[1+cos²(nπ/2)]An+sin²(nπ/2),n=1,2,3…… (1)求A3,A4,并求数列{An}的通项公式 (2)设Bn=A(2n-2)/A2n,Sn=B1+B2+...+Bn,证明:当n≥6时,|Sn-2|<1/n (1) A3 = [1+cos²(π/2)]A1+sin²(π/2) = A1+1 = 2 A4 = [1+cos²π]A2+sin²π = 2A2 = 4 n=2k-1时:A(2k+1)=A(2k-1)+1--->A.P.:A(2k-1)=k n=2k时,A(2k+2)=2A(2k)-------->G.P.:A(2k)=2^k (2) Bn = A(2n-2)/A(2n) = 1/2......
答:a1=1======================>a1+1=2(2¹) a2=2a1+1=3================>a2+1=4(2&s...详情>>
答:详情>>