Question

Find the sum:

8 over sigma symbol, k=1 below the symbol and (-1)^k+1,5k to the right of it.

Sorry the format is off, but I didnt know how else to type it in.

Thank you.

Answer 1

Here is how to type it.
The sum of (-1)^k +1.5k from k=1 to 8.

for eight terms, you can do this with your calc
k termvalue
1....0.5
2....4
3....3.5
4....7
5....6.5
6....10
7....9.5
8....13
See the pattern: each even add three to the previous even, and for the next odd, subtract .5
so predicting...
9....12.5 and you can check it.
Sum of the first 8 terms above, you can do that.
If you fish around, there are some generalized formulas for series such as this.

Answer 2

This is easy if you just break it up:

8
∑(-1)^k + 1.5k
1

= ∑(-1)^k + ∑1.5k
The first sum is -1+1-1+1... = 0, so

= ∑1.5k
= 1.5 ∑k
Now you know that

n
∑k = n(n+1)/2
1

so, your sum is just 1.5* 8*9/2 = 54