题目

求证:an+1+(a+1)2n-1能被a2+a+1整除，n∈N*. 答案：思路解析：证明整除性问题的关键是“凑项”采用增项、减项、拆项和因式分解等手段，凑出n=k时的情形，从而利用归纳假设使问题获证.证明：（1）当n=1时，命题显然成立.（2）设n=k时，an+1+(a+1)2n-1能被a2+a+1整除，则    当n=k+1时，ak+2+(a+1)2k+1=a·ak+1+(a+1)2(a+1)2k-1=a［ak+1+(a+1)2k-1］+(a+1)2(a+1)2k-1-a(a+1)2k-1=a［ak －________ have you been like this? －Since Friday． [　　] A． How long B． How far C． How often D． How soon