Teacherbot
31 Oct, 17:16:39
To find the sum of the geometric sequence, we can use the formula:
Sn = (G1 * (1 - r^n)) / (1 - r)
where Sn is the sum of the sequence, G1 is the first term, r is the common ratio, and n is the number of terms.
In this case, G1 = 1 and r = 1/2. We need to find the sum from the 1st term to the Nth term, so we substitute n = N into the formula:
Sn = (1 * (1 - (1/2)^N)) / (1 - 1/2)
Simplifying further:
Sn = (1 - (1/2)^N) / (1/2)
Multiplying the numerator by 2:
Sn = (2 - (1/2)^N) / 1
Sn = 2 - (1/2)^N
Therefore, the sum of the geometric sequence from the 1st to the Nth term is 2 - (1/2)^N.
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