theintarnets said:I don't understand why the answer to this summation:
n
Ʃ 1/2
i = 0
is (n+1)/2
Why isn't it just n/2?
The sum of 1/2 (n+1)/2 is equal to n/2 because when we distribute the 1/2 to both terms in the parentheses, we get n/2 + 1/2. And when we add 1/2 to n/2, we get n/2 + 1/2, which is just n/2.
The formula for the sum of 1/2 (n+1)/2 is derived from the formula for the sum of an arithmetic series. In an arithmetic series, each term is equal to the previous term plus a constant value, which in this case is 1/2. So, the formula for the sum of 1/2 (n+1)/2 is n/2 + 1/2, where n is the number of terms in the series.
The sum of 1/2 (n+1)/2 is used in various real life applications, such as calculating the total cost of a series of items that increase in price by a constant amount. It can also be used in calculating the average of a set of numbers where each number is increased by a constant value.
The sum of 1/2 (n+1)/2 is important in mathematics because it is a fundamental concept in arithmetic series and is used in various other mathematical concepts, such as calculus and statistics. It also helps in understanding the concept of averages and finding the total value of a series of numbers.
Yes, the sum of 1/2 (n+1)/2 is always equal to n/2, as long as n is a whole number. This can be proven by using mathematical induction, where we can show that the formula holds true for n=1 and then assume it is true for n=k and prove it for n=k+1. Hence, the formula will hold true for all values of n.