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29 tháng 1
\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)
\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)
\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)
11 tháng 4 2017
\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)
\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)
LM
Lê Minh Vũ
VIP
16 tháng 10 2021
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)
\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)
\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)
\(=\)\(\text{}\text{}\text{}\text{}\text{}\text{}\frac{\text{}\text{}\text{}\text{}\text{}\text{}3\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times7}{4\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times8\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times6}\)
\(=\)\(\frac{7\text{}\text{}\text{}\times4}{8\times6}\)
\(=\)\(\frac{7\times4}{4\times2\times6}\)
\(=\)\(\frac{7}{2\times6}\)
\(=\)\(\frac{7}{12}\)
7 tháng 6 2018
\(A\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)=\frac{8}{5}\)
\(A\times\frac{3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{4\times6}{5\times5}=\frac{8}{5}\)
\(A\times\frac{3\times2\times4\times3\times5\times4\times6}{2\times2\times3\times3\times4\times4\times5\times5}=\frac{8}{5}\)
\(A\times\frac{6}{2\times5}=\frac{8}{5}\)
\(A\times\frac{3}{5}=\frac{8}{5}\)
\(A=\frac{8}{5}:\frac{3}{5}\)
\(A=\frac{8}{3}\)
7 tháng 6 2018
ta có:
A = 8/5 : [(1 - 1/4) x ... x (1 - 1/5)]
= 8/5 : [3/4 x 8/9 x 15/16 x 24/25]
= 8/5 : 3/5
= 8/5 x 5/3
= 8/3
... là như đề bài nha!
DQ
3
TM
19 tháng 6 2016
\(K=\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)
\(K=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x\frac{35}{36}\)
tự rút gọn
\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}\)
\(=\frac{3x8x15x24}{4x9x16x25}\)
\(=\frac{3x2x4x3x5x4x2x3}{2x2x3x3x4x4x5x5}\)(chỗ này rút gọn đi)
\(=\frac{3}{5}\)