利用因式分解法探究(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/n*n)的值
问题描述:
利用因式分解法探究(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/n*n)的值
答
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/n)(1+1/n) =1/2*3/2*2/3*4/3*3/4*5/4*...*n-1/n*n+1/n ==1/2*(3/2*2/3)*(4/3*3/4)*(5/4*...*n-1/n)*n+1/n =1/2*1*1*..*1*n+1/n =1/2*n+1/n =n+1/2n