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If the sequence 1, 1/2, 1/4, 1/8, 1/16...
Find S1, S2 and Sn?
Awa Kals
Mar 26
If the sequence 1, 1/2, 1/4, 1/8, 1/16... Find S1, S2 and Sn?
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ChatGPT
Mar 26
To find S1, S2, and Sn for the given sequence, we need to find the sum of the first term, the sum of the first two terms, and the sum of the first n terms of the sequence.
The sequence is: 1, 1/2, 1/4, 1/8, 1/16...
S1 = 1
S2 = 1 + 1/2 = 3/2
Sn = 1 + 1/2 + 1/4 + 1/8 + ... + 1/2^(n-1)
To find Sn, we can use the formula for the sum of a geometric series:
Sn = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1, r = 1/2, and n is any positive integer.
Therefore, Sn = 1(1 - (1/2)^n) / (1 - 1/2)
Sn = (1 - 1/2^n) / (1/2)
Sn = 2(1 - 1/2^n)
Sn = 2 - 1/2^(n-1)
So, S1 = 1, S2 = 3/2, and Sn = 2 - 1/2^(n-1)
The sequence is: 1, 1/2, 1/4, 1/8, 1/16...
S1 = 1
S2 = 1 + 1/2 = 3/2
Sn = 1 + 1/2 + 1/4 + 1/8 + ... + 1/2^(n-1)
To find Sn, we can use the formula for the sum of a geometric series:
Sn = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1, r = 1/2, and n is any positive integer.
Therefore, Sn = 1(1 - (1/2)^n) / (1 - 1/2)
Sn = (1 - 1/2^n) / (1/2)
Sn = 2(1 - 1/2^n)
Sn = 2 - 1/2^(n-1)
So, S1 = 1, S2 = 3/2, and Sn = 2 - 1/2^(n-1)
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