Skip a number in a summation

Question

$$\sum_{n=1}^{10} n^2$$

Returns:

$1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100$

and I would like it to return:

$1 + 9 + 25 + 49 + 81 + 121 + 169 + 225 + 289 + 361$

How will I go about this and, more importantly, how does it work?

Answer 1

You are looking for $1^2 + 3^2 +5^2 +7^2 +9^2 +11^2+13^2+15^2+17^2 +19^2$

so whats wrong with

$$\sum_{n=0}^9(2n+1)^2$$

or

$$\sum_{n=1}^{10}(2n-1)^2$$

It's $2n$ because we are going up in twos

Answer 2

Yes, when it is easy, the short way is to transform the radical. Sometimes it is not possible because the argument would become too complex

There is not something like the step of a loop for ... next.

sum  0
for n = 1 to 10 step 2
    sum += n^2
next

A method without introducing a new argument is to qualify the index or to express it through a relation :

$S = \sum_{odd.n=1}^{10} n^2$

$U = \{ 1,3,...,9\}$ , $S = \sum_{n \in U} n^2 $