Express the sum below using summation notation. Use 1 as the lower limits of summation and i for the index of summation.
1/3+2/4+3/5+...+18/20
To express the sum using summation notation, we first need to determine the pattern in the terms of the sum.
Looking at the terms given, we can observe that the numerator of each term is equal to the index i, and the denominator is equal to (i + 2). Therefore, we can use the index i to represent both the numerator and the denominator.
Now, let's express the sum using summation notation:
Σ (i / (i + 2))
In this notation:
- Σ represents the uppercase Greek letter sigma, which stands for "sum."
- The expression to the right of the sigma represents the general term of the sum.
- i is the index of summation, which starts from 1 and increases by 1 each time until it reaches the upper limit.
- The lower and upper limits of summation are usually specified above and below the sigma, but since the question mentioned using 1 as the lower limit, we don't need to explicitly state it.
Thus, the given sum can be expressed using summation notation as:
Σ (i / (i + 2))