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.
Write the decimal number as a fraction
(over 1)
19.79 = 19.79 / 1
Multiplying by 1 to eliminate 2 decimal places
we multiply top and bottom by 2 10's
Numerator = 19.79 × 10 × 10 = 1979
Denominator = 1 × 10 × 10 = 100
Numerator / Denominator = 1979 / 100
Simplifying our fraction
= 1979/100
= 1979/100
= 19 79/100
A.b=15
B.m=18/11
C.b=28/3
D.k=18/7
E.j=3/2
F.m=7/2
Answer: 209.44
Step-by-step explanation:
V=πr2h 3=π·52·8 3≈209.43951
Answer:
About 7 times
Step-by-step explanation:
