Question

1+3+5+7+9+11+13+15+17+19=100 solve for the nth

Answer 1

Try to prove by induction that
\[\sum _{i=0}^n (2 i+1)=(n+1)^2
\]
In you case 19= 2 (9) +1, so n=9, n+1 =10, and (n+1)^2 = 10^2 =100