Question

Find the sum of the infinite series: (1/2)-(1/2)-(1/3)+(1/3)-(1/16)-(3/8)-(1/6)+(1/12)+(1/128)-(9/32)-(1/12)+(1/48)...

Answer 1

What is the pattern here?, i'm not seeing anything immediately.

Answer 2

yeah initially terms cancel but after the pattern is not very clearcut.

Answer 3

I'm not sure what the pattern is

Answer 4

The answer is -16/9 but I need to know how to solve the problem

Answer 5

- the 4 terms cancel
-(1/16)-(3/8)= -(7/16)
-(1/6)+(1/12)= -(1/12)
+(1/128)-(9/32)= -(35/128)
-(1/12)+(1/48)= -(3/48) = -(1/16) assume to -(7/16) from the top
this -(1/16) -(7/16) = -(8/16) = -(1/2) assume with second line result -(1/12)
-(1/12)-(1/2) = -(7/12)
do you can writing the next terms again ?

Answer 6

Loser any idea about this ?

Answer 7

No, I don't have any idea :(