计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)
问题描述:
计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)
答
(7 + 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)= (1/6) × (7 - 1)(7 + 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)= (1/6) × (7^2 - 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)= (1/6) × (7^4 - 1)(7^4 + 1)(7^8 + 1...1/6是哪来滴?因为前面乘了(7 - 1) ,也就是6,为了使等式的值不变,所以还要乘以 (1/6)