determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent

absolutely convergent

Step-by-step explanation:

given data

sin(n)/3^n

solution

we have given term

when n = 1

and we know that

value of sin(n) ≤ 1

so that we can say that

 ≤   or

here  is converges this is because common ratio in geometric series

here r is  and here it satisfy that -1 < r < 1

so it is converges

and

 is also similar

so it is  converges

and here no  term is

so we can say series is absolutely convergent

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)