Question

Find:
-1 + 1/3 -1/5 + 1/7 - 1/9 ....... till infinity.

Answer 1

looks like expansion of arctan

Answer 2

- pi/4 ?

Answer 3

Thats correct.
Proof?

Answer 4

taylor expansion of arctan(x), x= -1

Answer 5

Oh wait. its the geometric series one right?

Answer 6

http://www.wolframalpha.com/input/?i=expand+arctan%28x%29

Answer 7

Oh.
Riggghtttt.
Now that you mentioned it, we can use the geometric series to get this too.
Nicee.

Answer 8

i remember mukushla ... providing a nice solution of it. kinda forget though ...
try to get ... some series = arctan(x)

Answer 9

Oh i got it now.
Look.
Using sum of infinite GP,
=> 1/1+x^2 = 1 -x^2 + x^4 - x^6..........

Answer 10

int 1/(1+x^2) = arctan(x)

Answer 11

Where -x^2 is the common ratio.
Now we integrate it from 0 to 1.

Answer 12

To get this sum.

Answer 13

yep ... correct.

Answer 14

Thanks! :D

Answer 15

kinda had rev too ...

Answer 16

nice prob ...