3. (a) Given that lim, a2n = L and L, show that {an} is lim+00 a2n+1 = convergent and lim,→∞ an = L. (b) Let aj = 1 and an+1 1 and an+1 1+ 1 Write out the 1+an first eight terms of {an}. Use part (a) to show that lim,→00 an V2. This gives the continued fraction expansion 1 V2 = 1+ 1 2+ 2+...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.