Use a formula to find the sum of the series 1+2+4+8+⋯+1024 that has 11 terms.
not correct
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The series is a geometric series with a common ratio of 2. To find the sum, we can use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r)
Where:
S = sum of the series
a = first term of the series
r = common ratio
n = number of terms
In this case, the first term (a) is 1, the common ratio (r) is 2, and the number of terms (n) is 11. Substituting these values into the formula:
S = 1 * (1 - 2^11) / (1 - 2)
S = 1 * (1 - 2048) / (1 - 2)
S = 1 * (-2047) / (-1)
S = 2047
Therefore, the sum of the series 1+2+4+8+⋯+1024 with 11 terms is 2047.
The series is a geometric series with a common ratio of 2. We can use the formula for the sum of a geometric series to find the sum:
S = a * (1 - r^n) / (1 - r)
Where:
S = sum of the series
a = first term of the series
r = common ratio
n = number of terms
In this case, the first term (a) is 1, the common ratio (r) is 2, and the number of terms (n) is 11. Substituting these values into the formula:
S = 1 * (1 - 2^11) / (1 - 2)
S = 1 * (-1,023) / (-1)
S = 1,023
Therefore, the sum of the series 1+2+4+8+⋯+1024 with 11 terms is 1,023.