Question

How do you use sigma notation to write the sum for `[1-(1/6)^2]+[1-(2/6)^2]+...+[1-(6/6)^2]`?

Answer 1

`sum_(n=1)^6(1-(n/6)^2)`

Explanation:

If you look at the expression, the only thing that changes for each term is the number in red:
`[1-(color(red)(1)/6)^2]+[1-(color(red)(2)/6)^2]+...+[1-(color(red)(6)/6)^2]`.

It starts from one and is incremented by one until it reaches 6. Everything else stays the same. We just need to substitute the number that is changing by a variable: `sum_(n=1)^6(1-(n/6)^2)`.