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数列{1/cosncos(n+1)}前n项和怎么求啊?急.
题目详情
数列 {1/cosncos(n+1)}前n项和怎么求啊?急.
▼优质解答
答案和解析
∵sin1/cosncos(n+1)=sin(n+1-n)/cosncos(n+1)
=sin(n+1)cosn-cos(n+1)sinn/cosncos(n+1)
=tan（n+1)-tann．
∴1/cos0cos1+1/cos1cos2+…+1/cosncos(n+1)
=(tan1-tan0)/sin1+(tan2-tan1)/sin1+…+[tan(n+1)-tann]/sin1
=[tan(n+1)-tan0]/sin1
=tan(n+1)/sin1．
若不懂,晚安- -
=sin(n+1)cosn-cos(n+1)sinn/cosncos(n+1)
=tan（n+1)-tann．
∴1/cos0cos1+1/cos1cos2+…+1/cosncos(n+1)
=(tan1-tan0)/sin1+(tan2-tan1)/sin1+…+[tan(n+1)-tann]/sin1
=[tan(n+1)-tan0]/sin1
=tan(n+1)/sin1．
若不懂,晚安- -
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