题目

数列{an}的通项公式an=ncos,其前n项和为Sn,则S2012等于( ) (A)1006 (B)2012 (C)503  (D)0 答案：A解析:∵当n∈N*时, a4k+1=(4k+1)cos(2kπ+)=0, a4k+2=(4k+2)cos(2kπ+π)=-(4k+2), a4k+3=(4k+3)cos(2kπ+)=0, a4n+4=(4k+4)cos(2kπ+2π)=4k+4, ∴a4k+1+a4k+2+a4k+3+a4k+4=2. 则S2012=(a1+a2+a3+a4)+(a5+a6+a7+a8)+…+(a2009+a2010+a2011+a2012)=2×503=1006.Where we live，on the eastern shore of Maryland，the gentle waters run in and out like fingers slimming at the tips.The Canada geese know this place，as do the white swans and the ducks. In autumn，they come home for the winter. Once or twice each year，snow and frozen rain move into the area. When this happens，if the river is at its narrowest，there is a freeze which hardens the water to ice.One morning，a friend of mine set the breakfast table beside the huge window，which overlooked the Tred Avon River. Suddenly she leaned forward and cried out，“There is a goose out there.”We saw the figure of a large Canada goose，very still，its wings folded tight to its sides，its feet frozen into the ice.Then from the dark skies，she saw a line of swans. They floated from the top of the sky downward and at last landed on the ice. My friend was on her feet now，with one hand against her mouth，unbelieving. As the swans surrounded the frozen goose，she feared that life it still had might be pecked(啄) out by those great swan bills.Instead，those bills began to work on the ice. The long necks were lifted and curved down，again and again. It went on for a long time. At last，the goose’s head was lifted. Its body was pulled. Then the goose was free and stood on the ice. And the swans stood in the air watching. Then，as if it had cried，“I cannot fly.” Four of the swans came down around it. Their powerful beaks chipped off the ice held in the feathers. Slowly，the goose spread its wings as far as they would go，and moved slowly into the sky.This is a true story. I just think of it in the bad moment，and from it comes only one hopeful question：If so for birds，why not for man？1.Which would be the best title for the passage?A.Why Not for Man?B.Graceful SwansC.Swans’ Brave ActD.I Just Couldn’t Believe It!2.What happened to the Canada goose?A.It was deserted by other geeseB.It was stuck in the iceC.It was wounded and couldn’t flyD.It was lost in the water3.At first the author’s friend was worried that________A.the swans would not help the Canada gooseB.she didn’t care about this matter any moreC.the swans wouldn’t identify with the Canada gooseD.the swans would peck the Canada goose to death4.What did the swans do when they saw the Canada goose couldn’t fly?A.They chipped off the ice held in its feathersB.They waited patiently for the ice held in its feathers to meltC.They came down and lifted it up to the sky togetherD.They stayed with it and protected it