A series is defined by 8+4+2+1+1/2+1/4+...+1/32 Write the series in sigma notation
8+4+2+1+1/2+1/4+...+1/32
= 1/32 + 1/16 + ... + 4 + 8
sum = ∑ 2^(n - 6) for n= 1 to 9
To write the given series in sigma notation, we need to determine the pattern in the series and express it in terms of the index variable.
Looking closely at the terms, we can observe that each term is obtained by dividing the previous term by 2. Therefore, we can express the general term as:
a(n) = a(1)/2^(n-1)
where a(n) represents the nth term of the series.
Now, let's express the series using the sigma notation:
The given series starts with a(1) = 8. The terms continue up to a(6) = 1/32.
Σ(a(n)) from n = 1 to 6
Substituting the formula for a(n), we have:
Σ(a(1)/2^(n-1)) from n = 1 to 6
Thus, the series in sigma notation is:
Σ(8/2^(n-1)) from n = 1 to 6