add probs

The formula for the sum of n terms of this series (which , by the way , is the triangle numbers) will be a quadratic polynomial, so let $an^2 + bn + c = S_n$ . Then, $9a + 3b + c = 6$ , $4a + 2b + c = 3$ and $a + b + c = 1$ . Solving this system of equations gives $a = \frac{1}{2} , b = \frac{1}{2}$ and c = $0$ . Therefore , we have $S_n = \frac{n^2 + n}{2}$ . Plugging in $10$ into this gives $\frac{10^2 + 10}{2} = \frac{110}{2} = 55$ . Thank you for watching...

1. that means 1+2=3 3+3=6 6+4=10 10+5=15 15+6=21 21+7=28 28+8=36 36+9=45 45+10=55 thank you for watching.....