Some limiting sum questions... (1 Viewer)

[currysauce]

this i prolly easy for u... but since i am teaching myself


Write each as a recurring decimal (using gp limiting sum properties)

a) 0.23333333.....


b) 1.01515151515.....

 

[acmilan]

0.23333333.....
= 0.2 + 0.03 + 0.003 + 0.0003 + 0.00003 + ...

Consider 0.03 + 0.003 + 0.0003 + 0.00003 + ...

the common ratio is 0.1, which qualifies for a limiting series as it approaches infinity

S = a/(1-r) = 0.03/(1 - 0.1) = 0.03/0.9 = 3/90

Add the 0.2 to that which can be written as 1/5

so 1/5 + 3/90 = 18/90 + 3/90 = 21/90

So 0.23333333... = 21/90

Its the same method for the other question

1.01515151515.....
= 1 + 0.015 + 0.00015 + 0.0000015 + ...

ratio of 0.015 + 0.00015 + 0.0000015 + ... series is 0.01

S = a/(1-r) = 0.015/(1-0.01) = 0.015/0.99 = 15/990

Adding them give 1 + 15/990 = 990/990 + 15/990 = 1005/990

So 1.01515151515..... = 1005/990 = 201/198 = 67/66

 

[currysauce]

thankyou so much acmillan, you are a temperal god in my books

 

[Pace_T]

This is two unit.