\u7b49\u6bd4\u6570\u52171\uff0c2\uff0c4\uff0c8\uff0c16\u2026\u7684\u516c\u6bd4\u4e3a\u591a\u5c11\uff1f\u901a\u9879\u516c\u5f0f\u662f\u4ec0\u4e48\uff1f

\u7b49\u6bd4\u6570\u52171\uff0c2\uff0c4\uff0c8\uff0c16\u2026\u7684\u516c\u6bd4\u4e3a\u591a\u5c11\uff1f\u901a\u9879\u516c\u5f0f\u662f\u4ec0\u4e48\uff1f
2/1=4/2=8/4=...=2
\u516c\u6bd4\u4e3a2
an=2^(n-1)
\u901a\u9879\u516c\u5f0f\u662fan=2^(n-1)

\u6570\u52171\u3001 2\u3001 4\u3001 7\u3001 11\u3001 16\u7684\u901a\u9879\u516c\u5f0f\u662f(n^2-n+2)/2\u3002
\u89e3\uff1a\u4ee4\u6570\u5217an\u7684\u524d6\u9879\u5206\u522b\u4e3aa1=1\uff0ca2=2\uff0ca3=4\uff0ca4=7\uff0ca5=11\uff0ca6=16\u3002
\u90a3\u4e48a6-a5=5\uff0ca5-a4=4\uff0ca4-a3=3\uff0ca3-a2=2\uff0ca2-a1=1\uff0c\u5219\u53ef\u63a8\u51fa,
an-a(n-1)=n-1
a(n-1)-a(n-2)=n-2
a(n-2)-a(n-3)=n-
......
a4-a3=3
a3-a2=2
a2-a1=1
\u90a3\u4e48\u628a\u7b49\u5f0f\u7684\u5de6\u8fb9\u548c\u53f3\u8fb9\u5206\u522b\u76f8\u52a0\u53ef\u5f97\uff0c
an-a(n-1)+a(n-1)-a(n-2)+...+a3-a2+a2-a1=(n-1)+(n-2)+...+2+1
\u5316\u7b80\u53ef\u5f97\uff0can-1=(n-1)+(n-2)+...+2+1=n*(n-1)/2
\u6240\u4ee5an=n*(n-1)/2+1=(n^2-n+2)/2
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u6570\u5217\u7684\u5206\u7c7b
\u6570\u5217\u53ef\u5206\u4e3a\u6709\u7a77\u6570\u5217\u548c\u65e0\u7a77\u6570\u5217\u3001\u5468\u671f\u6570\u5217\u3001\u5e38\u6570\u6570\u5217\u7b49\u7c7b\u578b\u3002
2\u3001\u6570\u5217\u7684\u516c\u5f0f
\uff081\uff09\u901a\u9879\u516c\u5f0f
\u6570\u5217\u7684\u7b2cN\u9879an\u4e0e\u9879\u7684\u5e8f\u6570n\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u4ee5\u7528\u4e00\u4e2a\u516c\u5f0fan=f(n)\u6765\u8868\u793a\uff0c\u8fd9\u4e2a\u516c\u5f0f\u5c31\u53eb\u505a\u8fd9\u4e2a\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f\u3002
\u4f8b\uff1aan=3n+2
\uff082\uff09\u9012\u63a8\u516c\u5f0f
\u5982\u679c\u6570\u5217an\u7684\u7b2cn\u9879\u4e0e\u5b83\u524d\u4e00\u9879\u6216\u51e0\u9879\u7684\u5173\u7cfb\u53ef\u4ee5\u7528\u4e00\u4e2a\u5f0f\u5b50\u6765\u8868\u793a\uff0c\u90a3\u4e48\u8fd9\u4e2a\u516c\u5f0f\u53eb\u505a\u8fd9\u4e2a\u6570\u5217\u7684\u9012\u63a8\u516c\u5f0f\u3002
\u4f8b\uff1aan=a(n-1)+a(n-2)
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6570\u5217