Find out a new sequence
Assume {an} from n=1 to infinity converges to A, and find out a new sequence {bn} from n=1 to infinity by bn=(an+a(n+1))/2 for all n. Prove that {bn} from n=1 to infinity converges to A.
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Use the enhanced Euler's technique to approximate the solution to the initial value problem y= x/y, y(0) = ?1 at the point x =0.5, using steps of size h =0.25. Compare your answer with the actual solution (found by solving the equation) and with
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