Find S_11 for 1 + 2 + 4 + 8 + ...
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
The sum of the first 11 terms of the series 1 + 2 + 4 + 8 + ... has to be determined.
The terms of the sum form a geometric series with 1 being the first term and 2 as the common ratio. For a geometric series the sum of the first n terms is `a*(r^n -1)/(r - 1)`
Substituting the values from the problem `S_11 = 1*(2^11 - 1)/1 = 2048 - 1 = 2047`
The value of `S_11 = 2047`