Sec. 8.2 HW - Math Homework 8.2 Problem 12 Determine if the geometric series is convergent If it is convergent then find its sum 1 0.4 0.16 0.064 Notice

# Sec. 8.2 HW - Math Homework 8.2 Problem 12 Determine if the...

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Math Homework 8.2 Problem 12 Determine if the geometric series is convergent. If it is convergent, then find its sum: 1 + 0 . 4 + 0 . 16 + 0 . 064 + . . . Notice that this geometric series has first term a = 1 and multiplier r = 0 . 4 since 0 . 4 = 0 . 4 1 = 0 . 16 0 . 4 = 0 . 064 0 . 16 Because | 0 . 4 | < 1 this series converges with total sum 1 + 0 . 4 + 0 . 16 + 0 . 064 + . . . = 1 1 - 0 . 4 = 1 0 . 6 = 1 6 10 = 1 3 5 = 5 3 Problem 24 Determine whether the series is divergent or convergent. If it is convergent, then find its sum: summationdisplay n =1 bracketleftBig (0 . 8) n - 1 - (0 . 3) n bracketrightBig Notice this is the difference of two series: summationdisplay n =1 (0 . 8) n - 1 - summationdisplay n =1 (0 . 3) n The first series has initial term 1 and multiplier 0.8 whereas the second series has first term 0 . 3 and multiplier 0 . 3. Since both of these multipliers fall in the range needed for convergence the total