Question

S=1.2+2.3+3.4+4.5+...+38.39+39.40

Answer 1

S=1.2+2.3+...+39.40

3S=1.2.3+2.3.3+...+39.40.3

3S=1.2.(3-0)+2.3.(4-1)+...+39.40.(41-38)

3S=1.2.3-0.1.2+2.3.4-1.2.3+...+39.40.41-38.39.40

3S=(1.2.3+2.3.4+...+39.40.41)-(0.1.2+1.2.3+...+38.39.40)

3S=39.40.41-0.1.2

3S=39.40.41

S=\(\frac{39.40.41}{3}=21320\)