Final answer:
The expansion of the series sum from n equals 1 to 4 of 2 to the n plus 1 power is calculated by finding the value of 2 to the power of (n+1) for each n and adding them, resulting in 4 + 8 + 16 + 32, which sums up to 60.
Step-by-step explanation:
The student has asked about the expansion of the series sum from n equals 1 to 4 of 2 to the n plus 1 power. Expanding this series involves calculating the value of the expression 2(n+1) for each value of n from 1 to 4 and adding the results together.
Let's calculate each term:
- For n=1: 2(1+1) = 22 = 4
- For n=2: 2(2+1) = 23 = 8
- For n=3: 2(3+1) = 24 = 16
- For n=4: 2(4+1) = 25 = 32
The expansion of the series is the sum of these values:
4 + 8 + 16 + 32 = 60