a)
\(\left(1+\frac{1}{51}\right).\left(1+\frac{1}{52}\right).\left(1+\frac{1}{53}\right)...\left(1+\frac{1}{1963}\right)\)
\(=\frac{52}{51}.\frac{53}{52}.\frac{54}{53}...\frac{1964}{1963}\)
\(=\frac{1964}{51}\)
b)
\(\left(1+\frac{1}{400}\right).\left(1+\frac{1}{401}\right).\left(1+\frac{1}{402}\right)...\left(1+\frac{1}{2010}\right)\)
\(=\frac{401}{400}.\frac{402}{401}.\frac{403}{402}...\frac{2011}{2010}\)
\(=\frac{2011}{400}\)