- #1
student34
- 639
- 21
Homework Statement
2n
Ʃ (k)
k=1
The Attempt at a Solution
2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
student34 said:Homework Statement
2n
Ʃ (k)
k=1
The Attempt at a Solution
2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
Dick said:Sure. If you've shown the sum from 1 to n of k is n*(n+1)/2, then the sum to 2n is just 2n*(2n+1)/2. It's just substitution.
student34 said:So would this work too?
2n+1
Ʃ (k) = (2n+1)((2n+1)+1)/2
k=1
student34 said:Homework Statement
2n
Ʃ (k)
k=1
The Attempt at a Solution
2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
The subscript "n" in a summation expression denotes the number of terms being added together. In contrast, the 2n on top of the summation expression indicates that the number of terms being added is twice the value of n.
Yes, the value of 2n does affect the outcome of the summation. Since there are twice the number of terms being added, the result will be twice the value of the summation with just n terms.
Yes, the value on top of the summation expression can be replaced with any number. This will change the number of terms being added and thus affect the outcome of the summation.
The purpose of using 2n on top of the summation expression is to denote a specific pattern or sequence in the summation. It can also be used to simplify a complicated expression by reducing the number of terms being added.
There is no limit to the value of n in a 2n summation expression. The value of n can range from 0 to infinity, depending on the context of the problem or equation.