Question

(1+x分之1 )+ (1+x^2分之1 )+( 1+x^4分之4)+(1+x^8分之8)

Answer 1

如果题目是连加的话,应该不能用简便方法吧,只有是连乘才能用简便方法：

[1/(x+1)][1/(x^2+1)][4/(x^4+1)][8/(x^8)+1]

解,原式

={[1/(x-1)][1/(x+1)][1/(x^2+1)][4/(x^4+1)][8/(x^8)+1]}(x-1)

=[1/(x^2-1)][1/(x^2+1)][4/(x^4+1)][8/(x^8)+1]}(x-1)

=[1/(x^4-1)][4/(x^4+1)][8/(x^8)+1]}(x-1)

=4/(x^8-1)[8/(x^8)+1]}(x-1)

=32(x-1)/x^16-1

如果您的题目错了,那就是我这样做的.