Suppose the numbers a0,a1,a2,...,an satisfy the following conditions:
a0=1/2, a(k+1)=ak+(1/n)(ak)^2 ; k=1,2,...,n-1
Prove that 1-(1/n)<an<1.
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Calculate the value of , check that and use method of induction to prove the required.
by induction,i have
Let n=1, 0<an<1 (true)
we assume n=k is true.
i can't solve for n=k+1
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