题目

One day a Chinese student went to study English in England. His family name is Sun. It is the same as the word “sun”. England is a country with bad weather. It is often cloudy or misty, and it rains now and again. So the people there don’t get much sunshine in the whole year. When the Chinese student went to London, a tall English policeman with a large face opened his passport to examine(检查) it. The policeman was interested to find the Chinese name “sun” in the passport. He thought it was pronounced just like the English word “sun”，so he said to the Chinese student在数列{an}中，a1=1，an+1=2an+n，记bn=an+n+1，n∈N*．（Ⅰ）证明：数列{bn}是等比数列；（Ⅱ）记cn=2n+22bn+3，数列{cn}的前n项和为Sn，求证：Sn＜n+13．