Answer
a. $\frac{2\times3}{2} = 3$
b. $\frac{6\times7}{2} = 21$
c. $\frac{10\times11}{2} = 55$
d. $\frac{100\times101}{2} = 5050$
e. $\frac{1000\times1001}{2} = 500500$
Work Step by Step
a. $n=2$
$1+2=\frac{2\times3}{2} = 3$
b. $n=6$
$1+2+...+6=\frac{6\times7}{2} = 21$
c. $n=10$
$1+2+...+10=\frac{10\times11}{2} = 55$
d. $n=100$
$1+2+...+100=\frac{100\times101}{2} = 5050$
e. $n=1000$
$1+2+...+1000=\frac{1000\times1001}{2} = 500500$
The formula $\frac{N\times(N+1)}{2}$ works correctly on the given numbers.
