Question

Rút gọn : \(B=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)........\left(1+\frac{1}{20}\right)\)

Answer 1

\(B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{21}{20}\)

\(B=\frac{21}{2}\)

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Answer 2

\(B=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{20}\right)\)

\(\Rightarrow B=\left(\frac{2}{2}+\frac{1}{2}\right)\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{4}{4}+\frac{1}{4}\right)...\left(\frac{20}{20}+\frac{1}{20}\right)\)

\(\Rightarrow B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)

\(\Rightarrow B=\frac{21}{2}\)

Answer 3

B=\(\left(1+\frac{1}{2}\right)\).\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\)...\(\left(1+\frac{1}{20}\right)\)

B=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)=\(\frac{21}{2}\)

vậy B= 21/2

Answer 4

\(B=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).....\left(1+\frac{1}{20}\right)\)

   \(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{22}{20}\)

    \(=\frac{3.4.5....21}{2.3.4....20}\)

   \(=\frac{21}{2}\)