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.
I think you would use the equation 2x+1+33+90=180
These are the steps good luck
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
well then therefore
so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )
Since the order matters, it's a permutation of 7 letters, but mind you in
MOROCCO. you have 3 O's and 2 C's, Hence the arrangements are:
⁷P₇ /(3!2!) = 7!/(3!2!) = 5040/(3!2!) = 420 arrangements
