Thread: Sum of the squared of the integers

1. Sum of the squared of the integers

Here is another section I am having trouble with, it asks for:
the sum of the squares of the integers n: -12 less than or equal to n less than or equal 12.

the sum of the reciprocals of the integers n, where 100 less than or equal to n than or equal 200.

the sum of the cubes of the reciprocals of all integers, n where 1 is less than or equal to 50.

Am I supposed to put this in sigma notation or in a sum of a series?

I would appreciate it if you coud point me in the right direction.
Thank you!
Keith Stevens

2. Hello, Keith!

What were the instructions?
. . "Write as a sum of a series" or "Write in sigma notation" ?
I'll do it both ways . . .

The sum of the squares of the integers for $-12 \leq n \leq 12$.
$(\text{-}12)^2 + (\text{-}11)^2 + (\text{-}10)^2 + \cdots + 10^2 + 11^2 + 12^2 \;=\;\sum^{12}_{n=-12} n^2$

The sum of the reciprocals of the integers for $100 \leq n \leq 200$.
$\frac{1}{100} + \frac{1}{101} + \frac{1}{102} + \cdots + \frac{1}{200} \;=\;\sum^{200}_{n=100}\frac{1}{n}$

The sum of the cubes of the reciprocals for $1 \leq n \leq 50$.
$\left(\frac{1}{1}\right)^3 + \left(\frac{1}{2}\right)^3 + \left(\frac{1}{3}\right)^3 + \cdots + \left(\frac{1}{50}\right)^3\;=\;\sum^{50}_{n=1}\le ft(\frac{1}{n}\right)^3$

Simplified: . $\frac{1}{1^3} + \frac{1}{2^3} + \frac{1}{3^3} + \cdots + \frac{1}{50^3} \;=\;\sum^{50}_{n=1}\frac{1}{n^3}$

3. sum of squares

Thos examples are exactly what I need to finish the rest of the problems!
I am glad you can read my mind, sorry for not being more specific, I appreciate your insight.
Thank you again!!!!!!!!!
Keith Stevens