Question

B=(1+1/2).(1+1/3).....(1+1/59)

tính B

Answer 1

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.........\frac{60}{59}\)

\(=\frac{60}{2}=30\)

Answer 2

\(B=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)......\left(1+\frac{1}{59}\right)\)

\(\Rightarrow B=\left(\frac{2}{2}+\frac{1}{2}\right).\left(\frac{3}{3}+\frac{1}{3}\right).\left(\frac{4}{4}+\frac{1}{4}\right)......\left(\frac{59}{59}+\frac{1}{59}\right)\)

\(\Rightarrow B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{60}{59}\)

\(\Rightarrow B=\frac{3.4.5......60}{2.3.4.....59}\)

\(\Rightarrow B=\frac{60}{2}=30\)