Question

Tính tích:

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

 

Answer 1

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\cdot\cdot\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot\cdot\cdot\cdot\frac{100}{99}\)

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

Answer 2

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

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

\(=\frac{3.4.5...100}{2.3.4...99}\)

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

\(=50\)

Answer 3

hình như thiếu 1/98
đề đó đúng ko ( 1+ 1/2) x (1+ 1/3) x (1+ 1/4) x...x (1+ 1/98) x (1+ 1/99)

                                   Giải:

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

= 3/2 x 4/3 x 5/4 x … x 99/98 x 100/99

= (3 x 4 x 5 x … x 99 x 100) / 2 x 3 x 4 x … 98 x 99

Giản ước ta được:

= 100/2

= 50