19.(12分)解:(1)由数列{a,)的前n和S,=9.(a1 1知当n=1时,s1=a1(a 1,a1=S∴a1(a1-1)=0,又a1>0,所以a1=1……分当n>1时,an=S。-S-1≈9(an 1)_an-1(an-1 1)整理得:(an an-1)(an-an-1-1)=0因为an an1>0,所以有an-an1=1分所以数列{an}是首项a1=1,公差d=1的等差数列数列{an}的通项公式为an=a1 (n-1)d=n………………………………6分(Ⅱ)由an=n知:bn=log数列{b}的前n项和为h b b … b=1og22 log:3 lg … lgnog2(2×3×x…x×n 1)=1og2(n 2)-1……………………………8分令b十b2 b2 …十b。=k(k∈Z则有log2(n 2)-1=k,n=2* 1-2由n∈(0,2020),k∈Z知,k<10且k∈N10分所以区间(0,2020)内所有“优化数”的和为S=(22-2) (23-2) (24-2) … (210-2)=(22 23 24 2)-18-22(1-2)-18=21-22=2026…………………12分
书面表达One possible versionDear PeterI'm writing to invite you to see the Chinese Painting Exhibition to be held in our city.The exhibition will start at 8: 30 am on Saturday and last till 5: 00 pm on Sunday in the city museum It'ssaid that a large number of Chinese paintings, some of which are original works by famous painters like ZhangDaqian and Qi Baishi, will be on display. Besides, there will be various souvenirs to be sold. I know you re veryinterested in traditional Chinese culture, so I can t wait to tell you the news and hope we can go together.Looking forward to your reply.You
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