Question

Determine whether the series is convergent or divergent. ∞ (1 + 3^n) / 8^n n = 1

3.33/6.66 points v Previous Answers V SCALCETS 11.2.511.XP. Determine whether the series is convergent or divergent. 1 + 3n 80 I=1 O convergent O divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) Submit Answer

Answer 1

We are given an = 1+3h the series žan to here Let bn = 3 = (3) then. Then the series 2 bn = { (3)" converges 3/841 Now lim an tim 17 - lim 1+ 37.5 nto It' 10 - em nto since lim an alto nyoo bn 170 and {bo is convergent so to žan is convergent (by comparison test) Now since the series is a positive term series and it is convergent so it is absolutely convergent and hence we have, Now with § 2 is a geometric progression series common ration / so its sum is I if Earn is a GP senes with common ratio's the its sum is - pronded lrk! 11 a i-r similarly the sum , ( 32B) is 11 -3% = %. so you can see ft B-40456