I have a problem that I simply cannot solve. I have to put this series into summation notation, but I can't find the explicit formula! The series is
1 + 1/4 + 1/9 + 1/16 + 1/25
How do I even find the common difference in a series like that?
That is neither an arithmetic nor a geometric series. You are not asked
to find the sum of the series. You are only asked to find the summation
series. What you want is this:
Re-write the series
1 + + + +
as this:
+ + + +
That can be written this way:
k is the "dummy" variable, sometimes called the "index".
You can use another letter besides k if you like. The ∑
is the Greek letter "sigma" for "S" which stands for "SUM"
At the bottom of the ∑ is k=1 and the top is 5. At the
right of the ∑ you see a formula . This means
to start out by substituting 1 for k in the formula
getting which is 1. You write that down as the first
term.
So you have 1
Then you substitute k=2 in that formula
getting which is , so you put a + after the
1 and write that after it:
Now you have 1 +
Then you substitute k=3 in that formula
getting which is , so you put a + and write
that after it:
Now you have 1 + +
Then you substitute k=4 in that formula
getting which is , so you put a + and write
that after it:
Now you have 1 + + +
Then you substitute k=5 in that formula
getting which is , so you put a + and write
that after it:
Now you have 1 + + +
And you have finished because there is a 5 at the top of the ∑
which tells you when to stop.
But all you were asked to give as an answer is
Edwin