Write the sum (in sigma notation)
1 + 3/2 + 2 + 5/2 + 3 + 7/2 + 4
Sigma notation?
= 2/2 + 3/2 + 4/2 + ... 8/2
= ∑ (1+n)/2 for n = 1 to 7
This answer is not unique, there are many ways to express it
Consider the following sum
1/4*5+1/5*6+1/6*7+ ...+1/18*19
If it were written in sigma notation as
a=
b=
f(i)=
Sigma notation is a way to represent the sum of a series of terms in a concise and mathematical manner. It uses the Greek letter sigma (∑) to indicate the sum of terms. The terms are usually given as a general formula or expression, and the index variable specifies the range of values over which the terms are summed.
To write the given series in sigma notation, we need to analyze the pattern of the terms and find a general formula for each term based on the index.
Looking at the given series: 1 + 3/2 + 2 + 5/2 + 3 + 7/2 + 4
We can observe that the first term is 1, the second term is 3/2, the third term is 2, and so on. The pattern is a combination of whole numbers and fractions. The index variable for this series can be denoted by 'n', which represents the position of each term in the series.
Using this information, we can express the terms of the series in sigma notation as follows:
∑(k from 1 to n) [k + (2k-1)/2]
Let's break down this notation:
- The symbol ∑ represents the sum of terms.
- 'k' is the index variable that takes on integer values starting from 1 and going up to 'n'.
- The expression inside the square brackets [ ] represents the general formula for each term in the series. In this case, we have k (the whole number part) added to (2k-1)/2 (the fractional part).
Therefore, the given series 1 + 3/2 + 2 + 5/2 + 3 + 7/2 + 4 can be represented in sigma notation as:
∑(k from 1 to n) [k + (2k-1)/2]
Note: To find the sum of the series, you would substitute a specific value for 'n' and then evaluate the expression.