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

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.