Question

用数学归纳法(n+1)(n+2).(n+n)这是左边题目是当n=k到n=k+1时左端需增加的是

Answer 1

当n=k时,左侧=(k+1)(k+2)……(k+k)

当n=k+1时,左侧=(k+2)(k+3)……(k+k)(k+k+1)(k+1+k+1)

[(k+2)(k+3)……(k+k)(k+k+1)(k+1+k+1)]/[(k+1)(k+2)……(k+k)]

=(k+k+1)(k+k+2)/k+1

=2(2k+1)