Cách 1:
A = \(\frac{2}{1.2.3}\)+ \(\frac{2}{2.3.4}\)+ \(\frac{2}{3.4.5}\)+ .... + \(\frac{2}{36.37.38}\)+ \(\frac{2}{37.38.39}\)
A = \(\frac{3-1}{1.2.3}\)+ \(\frac{4-2}{2.3.4}\)+ \(\frac{5-3}{3.4.5}\)+ ... + \(\frac{38-36}{36.37.38}\)+ \(\frac{39-37}{37.38.39}\)
A = ( \(\frac{3}{1.2.3}\)- \(\frac{1}{1.2.3}\) )+ ( \(\frac{4}{2.3.4}\)-\(\frac{2}{2.3.4}\)) + ... + (\(\frac{38}{36.37.38}\)- \(\frac{36}{36.37.38}\)) + (\(\frac{39}{37.38.39}\)- \(\frac{37}{37.38.39}\))
A = ( \(\frac{1}{1.2}\)- \(\frac{1}{2.3}\)) + (\(\frac{1}{2.3}\) -\(\frac{1}{3.4}\) ) + ... + ( \(\frac{1}{36.37}\)- \(\frac{1}{37.38}\)) + ( \(\frac{1}{37.38}\)- \(\frac{1}{38.39}\))
A = \(\frac{1}{1.2}\)+ (-\(\frac{1}{2.3}\)+ \(\frac{1}{2.3}\)) + (-\(\frac{1}{3.4}\)+ \(\frac{1}{3.4}\)) + ..... + ( -\(\frac{1}{37.38}\)+\(\frac{1}{37.38}\)) - \(\frac{1}{38.39}\)
A = \(\frac{1}{1.2}\)+ 0 + 0 + 0 +... + 0 - \(\frac{1}{38.39}\)
A = \(\frac{1}{1.2}\)- \(\frac{1}{38.39}\)= \(\frac{741}{1482}\)- \(\frac{1}{1482}\)= \(\frac{740}{1482}\)=\(\frac{370}{741}\)