Question

2	+	2	+ … +	2	=
4 x 6		6 x 8		188 x 190

Answer 1

\(\dfrac{2}{4\times6}+\dfrac{2}{6\times8}+...+\dfrac{2}{188\times190}\\ =\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+....+\dfrac{1}{188}-\dfrac{1}{190}\\ =\dfrac{1}{4}-\dfrac{1}{190}\\ =\dfrac{93}{380}\)

Answer 2

\(\dfrac{2}{4\times6}+\dfrac{2}{6\times8}+...+\dfrac{2}{188\times190}\)

\(=\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{188}-\dfrac{1}{190}\)

\(=\dfrac{1}{4}-\dfrac{1}{190}\)

\(=\dfrac{190-4}{760}\)

\(=\dfrac{186}{760}=\dfrac{93}{380}\)