Question

What is the sum of the first 50 natural numbers? How to solve it without adding 50 digits?

Answer 1

$1+2+3+4+5+\dots+50\\\\1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\\where\ a_1=1\ and\ d=1\\\\Sum:S_n=\frac{a_1+a_n}{2}\cdot n\\\\S_{50}=\frac{1+50}{2}\cdot50=51\cdot25=1275\leftarrow solution$

Answer 2

Look at the first one and the last one:                  1 + 50 = 51
Look at the second one and the second-last one:  2 + 49 = 51
Look at the third one and the third-last one:           3 + 48 = 51

Every pair you construct in this way adds up to 51 .

There are ( 50/2 ) = 25 pairs.

They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275