Question 608591
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?
<pre>
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 + {{{1/4}}} + {{{1/9}}} + {{{1/16}}} + {{{1/25}}} 

as this:

{{{1/1^2}}} + {{{1/2^2}}} + {{{1/3^2}}} + {{{1/4^2}}} + {{{1/5^2}}}

That can be written this way:

{{{sum(1/k^2,k=1,5)}}}

k is the "dummy" variable, sometimes called the "index".
You can use another letter besides k if you like.  The &#8721;
is the Greek letter "sigma" for "S" which stands for "SUM" 
At the bottom of the &#8721; is k=1 and the top is 5.  At the
right of the &#8721; you see a formula {{{1/k^2}}}.  This means
to start out by substituting 1 for k in the formula {{{1/k^2}}}
getting {{{1/1^2}}} which is 1.  You write that down as the first
term.

So you have 1

Then you substitute k=2 in that formula {{{1/k^2}}}
getting {{{1/2^2}}} which is {{{1/4}}}, so you put a + after the
1 and write that after it:

Now you have 1 + {{{1/4}}}

Then you substitute k=3 in that formula {{{1/k^2}}}
getting {{{1/3^2}}} which is {{{1/9}}}, so you put a + and write 
that after it:

Now you have 1 + {{{1/4}}} + {{{1/9}}}

Then you substitute k=4 in that formula {{{1/k^2}}}
getting {{{1/4^2}}} which is {{{1/16}}}, so you put a + and write 
that after it:

Now you have 1 + {{{1/4}}} + {{{1/9}}} + {{{1/16}}}

Then you substitute k=5 in that formula {{{1/k^2}}}
getting {{{1/5^2}}} which is {{{1/25}}}, so you put a + and write 
that after it:

Now you have 1 + {{{1/4}}} + {{{1/9}}} + {{{1/25}}}

And you have finished because there is a 5 at the top of the &#8721;
which tells you when to stop.

But all you were asked to give as an answer is

{{{sum(1/k^2,k=1,5)}}}

Edwin</pre>