Question

TÍNH : 
\(\left(1+\frac{1}{2}\right)\)\(x\left(1+\frac{1}{3}\right)\)\(x\left(1+\frac{1}{4}\right)\)\(x......x\left(1+\frac{1}{98}\right)x\left(1+\frac{1}{99}\right)\)

Answer 1

\(\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times....\times\left(1+\frac{1}{98}\right)\times\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times....\times\frac{99}{98}\times\frac{100}{99}\)

\(=\frac{3\times4\times5\times...\times99\times100}{2\times3\times4\times....\times98\times99}\)

\(=\frac{100}{2}=50\)

Answer 2

(1+1/2).(1+1/3).(1+1/4)....(1+1/98).(1+1/99)

=3/2.4/3.5/4...99/98.100/99

=3.4.5....99.100/2.3.4....98.99

=100/2

=50