SOLUTION: 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

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