(5+1)(5的平方+1)(5的4次方+1)......(5的n次方+1)

反复利用平方差公式 (5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)...(5^n+1) =1/4*(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)...(5^n+1) =1/4*(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)....(5^n+1) =...... =1/4*(5^n-1)*(5^n+1) =1/4(5^2n-1)