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let-p-n-x-1-k-1-k-x-k-1-prove-that-the-equation-p-n-x-0-have-only-one-solution-x-n-0-1-2-prove-that-x-n-is-decreasing-and-minored-by-1-2-3-prove-that-lim-n-x-n-1-2-




Question Number 30193 by abdo imad last updated on 17/Feb/18
let p_n (x)=−1 +Σ_(k=1) ^k  x^k   1) prove that the equation p_n (x)=0 have only one   solution x_n ∈[0,1] .  2) prove that (x_n ) is decreasing and minored by (1/2)  3) prove that lim_(n→∞)  x_n =(1/2) .
letpn(x)=1+k=1kxk1)provethattheequationpn(x)=0haveonlyonesolutionxn[0,1].2)provethat(xn)isdecreasingandminoredby123)provethatlimnxn=12.

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