1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1/ 2^13=

Question

1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1/ 2^13=?

haas_mba07 · Answer

Sum = 15/2^13

Given

1/2^10 + 1/2^11 + 1/2^12 + 1/2^13

= 1/2^13 x (2^3+ 2^2 + 2^1 + 1) 

= 1/2^13 x (8+4+2+1)

= 15/2^13

lan583 · Answer

How did you arrive with the bold numbers?Thanks

haas_mba07 · Answer

Take just two of the numbers

1/2^13 + 1/2^10

Taking 1/2^13 common as follows: 

We know : a^b x a^c = a^(b+c)

Similary

1/2^10 = 1/2^(13-3) = 1/(2^13 x 2^(-3)) 
= 2^3/2^13

Note than for any number 1/a^b = a^(-b)

Therefore the equation: 
1/2^13 ( 1+ 2^3)

Hope this helps.

ps_dahiya · Answer

Or alternatively you can do it like this:
1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1/ 2^13

 = 1/ 2^10 (1+ 1/ 2 + 1/4 + 1/8)
 = 1/ 2^10 (15/8)
 = 15/(2^10 * 2^3)
 = 15/2^13

GMATT73 · Answer

Whereas Haas' method is more textbook, Dahiya's is more efficient. Both are smooth. 8-)

Yurik79 · Answer

1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1/ 2^13= can be written as
2^-10+2^-11+2^-12+2^-13=
2^-10*(1+2^-1+2^-2+2^-3)=
2^-10*(1+1/2+1/4+1/8)=
2^-10*(15/8)=--->15/8 can be written as 15/(2^-3)
hence the answer is
15*2^13

1/ 2^10 + 1/ 2^11 + 1/ 2^12 + 1/ 2^13=

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