Find the sum of the geometric sequence. three divided by two, three divided by eight, three divided by thirty two, three divided by one hundred and twenty eight, three divided by five hundred and twelve

we have that

[3/2,3/8,3/32,3/128,3/512]

the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]

=(1/512)*[256*3+64*3+16*3+4*3]

=(3/512)*[256+64+16+4]

=(3/512)*[340]

=(1020/512)

=255/128> 1.9922

the answer is

1.9922

another way to calculate it 

is through the following formula

∑=ao*[(1-r^n)/(1-r)]

where 

ao> is the first term

r> is the common ratio between terms

n> is the number of terms

ao=1.5

r=1/4> 0.25

n=5

so

∑=1.5*[(1-0.25^5)/(1-0.25)]> 1.99

Step-by-step explanation: we have that

[3/2,3/8,3/32,3/128,3/512]

the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]

=(1/512)*[256*3+64*3+16*3+4*3]

=(3/512)*[256+64+16+4]

=(3/512)*[340]

=(1020/512)

=255/128> 1.9922

the answer is

1.9922

another way to calculate it 

is through the following formula

∑=ao*[(1-r^n)/(1-r)]

where 

ao> is the first term

r> is the common ratio between terms

n> is the number of terms

ao=1.5

r=1/4> 0.25

n=5

so

∑=1.5*[(1-0.25^5)/(1-0.25)]> 1.99

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x