sequences/series question (1 Viewer)

[Arithela]

Find the sum of the powers of 2 from 1 to 1024 inclusive. Can somebody explain how to do this?​

 

[aalex]

I’d say that the question is asking the sum of: 1 + 2 + 4 + 8 + … + 1024, which are powers of 2 from 1 = 2<SUP>0</SUP> to 1024 = 2<SUP>10</SUP>.
So we have a geometric series with a =1, r =2 and n = 11 (from 0 to 10 there are 11 terms).
S<SUB>11</SUB>= 1(2<SUP>11</SUP> – 1)/(2-1)=2<SUP>11</SUP> – 1 = 2047

:wave:

 

[Arithela]

that's correct, thank you.