Series and Sequences Q (1 Viewer)

[OL_O]

Can the sum of a limiting series be negative?

 

[InteGrand]

Can the sum of a limiting series be negative?

Yes. E.g. .

 

[OL_O]

could you please explain to my why the series

-1/27 + 1/9 - 1/3 doesn't have a limiting sum?

When i put a= -1/27 and r= -3 into the formula a/1-r i got -1/108 but the answers said that the limiting sum cant be found?

 

[InteGrand]

could you please explain to my why the series

-1/27 + 1/9 - 1/3 doesn't have a limiting sum?

When i put a= -1/27 and r= -3 into the formula a/1-r i got -1/108 but the answers said that the limiting sum cant be found?

When the common ratio has absolute value more than (or equal to) 1 (i.e. ), then there is no limiting sum (the series doesn't converge). The series will converge if and only if .

So in your question, since r was -3, and -3 has absolute value greater than 1, the series won't converge.

 

[faisalabdul16]

could you please explain to my why the series

-1/27 + 1/9 - 1/3 doesn't have a limiting sum?

When i put a= -1/27 and r= -3 into the formula a/1-r i got -1/108 but the answers said that the limiting sum cant be found?

That's because

<a href="http://www.codecogs.com/eqnedit.php?latex=|r|&space;<&space;1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?|r|&space;<&space;1" title="|r| < 1" /></a>

 

[OL_O]

When the common ratio has absolute value more than (or equal to) 1 (i.e. .

So in your question, since r was -3, and -3 has absolute value greater than 1, the series won't converge.

Oh now i understand, Thank you