Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer:
6:3
Step-by-step explanation:
Answer:
w>0.9
Step-by-step explanation:
7.2-3w<4.5
-7.2 -7.2
-3w<-2.7
/-3 /-3
w>0.9
The inequality switches when divided by a negative.
-hope it helps
Answer: 6 years
Step-by-step explanation:
Formula to calculate compound amount:
, where P= Principal , r=rate of interest, t= time
Given: P = £400, r = 3% = 0.03 , A= 475
Required equation: 

Taking log on both sides , we get

Hence, he needs to invest the money for 6 years to get atleast £475.