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let-a-sequence-be-difined-as-a-n-a-n-1-2cos-a-n-1-2-2sin-a-n-1-2-1-a-0-0-find-lim-n-a-n-




Question Number 210549 by universe last updated on 12/Aug/24
let a sequence be difined as   a_n = a_(n−1)  + ((2cos ((a_(n−1) /2)))/(2sin ((a_(n−1) /2))−1))  , a_(0 ) = 0  find lim_(n→∞)  a_(n )  = ?
letasequencebedifinedasan=an1+2cos(an12)2sin(an12)1,a0=0findlimnan=?
Answered by aleks041103 last updated on 16/Aug/24
Commented by aleks041103 last updated on 16/Aug/24
f(x) = x + ((2cos(x/2))/(2sin(x/2)−1))    a_n =f(a_(n−1) )    seems like a_n →−π  the proof seems to be a bit difficult
f(x)=x+2cos(x/2)2sin(x/2)1an=f(an1)seemslikeanπtheproofseemstobeabitdifficult

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