Question

Calculate 2+4+6...+2n for n= 1,2, ..., 6

Answer 1

For n = 1, the value of 2n is 2 * 1 = 2, so the sentence is just the number 2:

$\begin{gathered} n=1\colon \\ 2=2 \end{gathered}$

For n = 2, we have:

$\begin{gathered} n=2\to2n=2\cdot2=4 \\ 2+4=6 \end{gathered}$

Then, for n = 3, 4, 5 and 6, we have:

$\begin{gathered} n=3\to2n=2\cdot3=6 \\ 2+4+6=12 \\ \\ n=4\to2n=2\cdot4=8 \\ 2+4+6+8=20 \\ \\ n=5\to2n=2\cdot5=10 \\ 2+4+6+8+10=30 \\ \\ n=6\to2n=2\cdot6=12 \\ 2+4+6+8+10+12=42 \end{gathered}$

So the answers are 2, 6, 12, 20, 30 and 42.