Final answer:
The summation Σ from n=1 to 4 of (1/6)^(n-1) is calculated by plugging the values of n from 1 to 4 into the formula and adding the results, resulting in a final sum of 259/216 or roughly 1.1991 as a decimal.
Step-by-step explanation:
To evaluate the summation Σ from n=1 to 4 of (1/6)^(n-1), you simply plug in the values of n from 1 to 4 into the formula and add the results together:
- For n=1: (1/6)^(1-1) = (1/6)^0 = 1
- For n=2: (1/6)^(2-1) = (1/6)^1 = 1/6
- For n=3: (1/6)^(3-1) = (1/6)^2 = 1/36
- For n=4: (1/6)^(4-1) = (1/6)^3 = 1/216
Now, add these values together:
1 + 1/6 + 1/36 + 1/216 = 216/216 + 36/216 + 6/216 + 1/216 = 259/216 or approximately 1.1991 when expressed as a decimal.