What is the limit of the infinite series?

∞

∑ ( 3n^5/4n^5+1)

n=1

enter your answer in the box. enter any fraction as a simplified fraction.

does not exist

Step-by-step explanation:

According to the divergence test, for an infinite series ∑ aₙ, the series diverges if lim(n→∞) aₙ ≠ 0.

Applying the divergence test here:

lim(n→∞) (3n⁵ / (4n⁵ + 1)) = 3/4

This is not 0, so the series does not converge, meaning the sum does not exist.

step-by-step explanation:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2