求:(5+1)(5的平方+1)(5的四方+1)(5的八方+1)的值
问题描述:
求:(5+1)(5的平方+1)(5的四方+1)(5的八方+1)的值
答
巧算:原式=(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)/4(因为前面多乘了(5-1),得除掉)=(5^2-1)(5^2+1)(5^4+1)(5^8+1)/4=(5^4-1)(5^4+1)(5^8+1)/4=(5^8-1)(5^8+1)/4=(5^16-1)/4
答
38146972656
答
(5+1)(5^2+1)(5^4+1)(5^8+1)=[(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)]÷(5-1)=[(5^2-1)(5^2+1)(5^4+1)(5^8+1)]÷(5-1)=[(5^4-1)(5^4+1)(5^8+1)]÷4=[(5^8-1)(5^8+1)]÷4=(5^16-1)/4