已知数列XN满足,X(N+1)=XN-X(N-1)(N大于等于2),X1=A,X2=B,AN=X1+X2+..+XN..

问题描述:

已知数列XN满足,X(N+1)=XN-X(N-1)(N大于等于2),X1=A,X2=B,AN=X1+X2+..+XN..
X100=?S100=?

X1=AX2=BX3=X2-X1=B-AX4=X3-X2=B-A-B=-AX5=X4-X3=-A-B+A=-BX6=X5-X4=-B-(-A)=A-BX7=X6-X5=A-B-(-B)=A =X1可见Xn是循环的,每6项循环一次(1)100÷6=16余4所以X100=X4=-A(2)∵S6=A+B+B-A-A-B+A-B=0∴S100=16S6+S4=X...