Question

E=1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+............+1/200(1+2+......+200)

Answer 1

\(E=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{200}\left(1+2+...+200\right)\)

\(E=1+\frac{1}{2}.\frac{\left(1+2\right).2}{2}+\frac{1}{3}.\frac{\left(1+3\right).3}{2}+...+\frac{1}{200}.\frac{\left(1+200\right).200}{2}\)

\(E=1+\frac{1+2}{2}+\frac{1+3}{2}+...+\frac{1+200}{2}\)

\(E=1+\frac{3}{2}+\frac{4}{2}+...+\frac{201}{2}\)

\(E=\frac{2+3+4+...+201}{2}=\frac{\left(201+2\right).200:2}{2}\)

\(E=10150\)