高一 数列
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高一数列高一数列 高一数列a(1)=1,a(n+1)=a(n)+1/[(n+1)(n+2)]=a(n)+1/(n+1)-1/(n+2),a(n+1)+1/(n+2)=a(n)+1/(n+1)
高一 数列
高一 数列
高一 数列
a(1)=1,
a(n+1) = a(n) + 1/[(n+1)(n+2)]
= a(n) + 1/(n+1) - 1/(n+2),
a(n+1) + 1/(n+2) = a(n) + 1/(n+1),
{a(n)+1/(n+1)}是首项为a(1) + 1/2 = 3/2,的常数数列.
a(n) + 1/(n+1) = 3/2,
a(n) = 3/2 - 1/(n+1).
a(1) = 3/2 - 1/2 = 1,
a(2) = 3/2 - 1/3 = 7/6,
a(3) = 3/2 - 1/4 = 5/4,
a(4) = 3/2 - 1/5 = 13/10.
a(5) = 3/2 - 1/6 = 4/3.