Given the linear system 3x+4)=s 6x+8) =I. (a) Determine particular values for l' and I so Ihal the system is consistent. (II) Dtlennine p.uticulal values fOJ 1 and I so thai the system is inconsistent. (c) What relationship between the values of s and I will guarantee Ihat Ihe system is consistent?

11.1-11.4 11.1 Sequences Sequence- can be thought of as a list of numbers written in a definite order. a1, a2, a3,……. ax EX.) (n^2)from n=1 to n=infinity {1, 4, 9, 16…..} EX.)((-1)^n)/(n+3) { 1/5, -1/6, 1/7, -1/8} Notice that because of the negative 1 to the n the series alternates from positive to negative A sequence has a limit L. This shows what all the numbers are going to in the sequence. Lim as n goes to infinity of (an)=L EX.)lim as n goes to infinity of (1/n)=0 As n gets bigger the denominator is getting large and the denominator is staying the same so the number is getting close and close to 0 If the sequence has a limit then the sequence converges. Otherwise, the sequence diverges. Like the sequence n^2 as n gets large the numbers go to infinity making the sequence divergent. 11.2 Series Infinite series- is the sum of the terms of a sequence. Given a series the sum of (an) from n=1 to infinity… a1+ a2+ a3+….. let sn be the partial sum. If the sequence (sn) is convergent and the limit of sn exists as a real number then the series is convergent. EX.) the sum between n=1 and infinity of (n+1)/n^2… 2/1+3/4+4/9… So to see if this series is divergent or convergent we can take the limit as n goes to infinity of (n+1)/n^2 Because of hospitals rule saying we cant have infinity/infinity, we can take the derivative of the numerator and denominator and take the limit of that. This leaves us