What is sum of the infinite geometric series for 1 -1/5 + 1/25 - 1/125 +

5/6

Step-by-step explanation:

Sum of infinite geometric series is given by formula a/(1-r).

where a is the first term

and r is the common ratio of geometric term.

Common ratio for a geometric series is given by  nth term/(n-1)th term.

Given series is

1 -1/5 + 1/25 - 1/125 +

step 1 : calculate r

for r lets use second and first term

2nd term = -1/5

1st term = 1

r = 2nd term/1st term = (-1/5) / 1 = -1/5

sum of this series = a/(1-r)

substituting a with 1 and r with -1/5, we have

sum of this series = 1/(1-(-1/5)) = 1/(1+1/5)

=> sum of this series =  1/((5+1)/5)

=> sum of this series =  1/ (6/5) = 5/6

sum of the infinite geometric series 1 -1/5 + 1/25 - 1/125 + is 5/6

answer

false

explanation

these practices describe the manner the land use outcome is attained. land management methods implemented by corporations are a mandatory because they are a driver for better land use results economically, socially and environmentally. corporations are required to understand the connection between land use , and land management practices to support sustainable land use policies

(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