归纳：An=A1+(A2-A1)+.+(An-An-1)你要倒过来看就会明白了.An=(An-An-1)+(An-1-An-2)+.+(A2-A1)+A1例题:若数列An满足A1=1,An=3^n-1(3的n-1次方)+An-1,n>=2.
求A2,A3;证明An=二分之3^n-1（二分之3的N次方减1)[解析]因为A1=1,所以A2=4,A3=13(2)由已知得,An-An-1=3^n-1
所以An=(An-An-1)+(An-1-An-2)+.+(A2-A1)+A1=3^n-1+3^n-2+.+3+1=二分之3的N次方减1[本题是累加法和消项法并用]