Question

Find the sum /x+1 + 1/1+x^2 + 1/1+x^4+1/1+x^8............1/1+x^ 2^n

Answer 1

yoooooooooo ^_^
 this question can be solve by reducing the series by adding or subtracting some variables
your question is just like that
↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↓↔↔↔↔↔↔↔↔↔↔↔↔↔↔
1/(1+x) + 1/ 1+x^2 + 1/1+x^4 + ............................................1/1+x^2^2n
now i will just add some thing to reduce let me think ............................................................................................................................................................................................................................................................................................................................................................... ahh han got it 
if i do add and subtract this quantity
1/x-1 +1/1-x + 1+x + 1/ 1+x^2+ ...................................................1/1+x^2^2n
1/x-1   1/1-x + 1/1+x + /1+x^2+................................................1/ 1+x^2n
now let me think i will just take lcm of 1/1-x + 1/1+x to check that if series is reducing than i will reduce the whole series by doing same thing
1/1-x +1/1+x=  (1+x-x+1)/1+x^2 = 2/1-x^2 yes we can say that this idea is working so we can reduce the whole equation  dude ;) ahhhh
1/1-x + 2/1-x^2+ 1/1+x^2 .......................................
1/1-x +4/1-x^4+ 4/1+x^4 ........................................
and then finnaly we get
1/1-x  + 2^2n/1+x^2^n hope this will help u this question was really tough none can think too much logically  hope this will help others tooo ^_^