series-answers

Solutions to the Sample Problems from Unit 11B: Sequences & Series
(click here to return to the problem set) > b) 1.1 + 1.32 + 1.584 + 1.9008... The ratio is 1.32/1.1= 1.2. The absolute value of this ratio is >1, so the series is DIVERGENT and does not have a sum.
 * 1) Not possible to solve, the sum cannot be determined because the common ratio is greater than 1 and therefore it diverges
 * 2) 5*26*26
 * 3) The sum of the first n odd numbers is n^2. So the sum of the first 37 odd numbers is 37^2, or 1369.
 * 4) Although we don't know how many numbers are in the series, we can still solve the problem. Sum= (ratio(last term) - (First term))/(first term) The ratio is 2, the first term is 1, and the last term is 1024, so S= (2 x 1024 - 1)/1 = 2047
 * 5) a) 1/2 + 3/8 + 9/32.... We have to first determine the ratio to decide whether the series is divergent or convergent. The ratio is (3/8)/(1/2), which is 3/4. The absolute value of this ratio is <1, so the series is CONVERGENT and a sum can be determined. The sum is (first term)/ (1-ratio). s= (3/8)/ (1-3/4), which equals 3/2.
 * 1) Answer=2. It is a convergent series.