rewrite the series in sigma notation 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024
notice your numbers are simply powers of 2, with the exponent at 0 for
n = 1
∑ 2^(n-1) for n = 1 to 11
I think I'd prefer
10
∑ 2^n
n=0
To rewrite the given series in sigma notation, let's analyze the pattern.
The series can be written as the sum of powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Notice that each term is obtained by multiplying the previous term by 2.
We can express this pattern using the sigma notation (Σ). The general form of the series is:
Σ(2^n) from n = 0 to 10
Here, n represents the position of each term in the series. It starts at 0 because we are using the terms' positions, not their values.
Therefore, the series "1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024" can be written in sigma notation as:
Σ(2^n) from n = 0 to 10