Question

Hello! I need help on the following question(s), I’m aware of the one question policy and I tried the first couple of questions to the best of my ability but it seems that the questions are connected.

Answer 1

No 11.

To know that the formula works, we can test it:

`\sum ^n_(k\mathop=1)k`

At n=2, the triangular sum will be:

`\sum ^2_{k\mathop{=}1}k=1+2=3`

And when we count the dots on the second term, we see that the sum is 3, so therefore the formula works.

Let us test another.

At n=3, the triangular sum will be:

`\sum ^3_{k\mathop{=}1}k=1+2+3=6`

And when we count the dots on the third term, we see that the sum is 6, so therefore the formula works.

No 12.

The graph is plotted in the image below: