The following series are geometric series or a sum of two geometric series. Determine whether each series converges or not. For the series which converge, enter the sum of the series. For the series which diverges enter "DIV" (without quotes).
a. Σ[infinity] n=1 6^n/5^n =
b. Σ[infinity] n=2 1/2^n =
c. Σ[infinity] n=5 5^n/6^n =

a. Does not converge

b. Converges. And the sum would be 0.5

c. Converges. And the sum would be 2.411

Step-by-step explanation:

Remember that a series of the type

Converges when  

a.

Therefore it does not converge.

b.  

Therefore it converges. And the sum would be

c.

Therefore it converges. And the sum would be

49%

step-by-step explanation:

when you realize that you dont know just realize i just took a test and im so smart

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week