giải giúp mk vs

\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)

\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}=\frac{3.8.15.24.35}{4.9.16.25.36}=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}\)

\(=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{2.2}=\frac{7}{4}\)

dat off roi

3/4x8/9x15/16x24/25x35/36=7/12

lời giải luôn nhé

\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)

\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)

\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)

\(=\)\(\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\frac{\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times7}{4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times8\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6}\)

\(=\)\(\frac{7\text{​​}\text{​​}\text{​​}\times4}{8\times6}\)

\(=\)\(\frac{7\times4}{4\times2\times6}\)

\(=\)\(\frac{7}{2\times6}\)

\(=\)\(\frac{7}{12}\)

\(A\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)=\frac{8}{5}\)

\(A\times\frac{3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{4\times6}{5\times5}=\frac{8}{5}\)

\(A\times\frac{3\times2\times4\times3\times5\times4\times6}{2\times2\times3\times3\times4\times4\times5\times5}=\frac{8}{5}\)

\(A\times\frac{6}{2\times5}=\frac{8}{5}\)

\(A\times\frac{3}{5}=\frac{8}{5}\)

\(A=\frac{8}{5}:\frac{3}{5}\)

\(A=\frac{8}{3}\)

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!

\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)

\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)

\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)

a:Sửa đề: 1x3+2x4+...+99x101

\(=1\times\left(1+2\right)+2\times\left(2+2\right)+\cdots+99\times\left(99+2\right)\)

\(=\left(1\times1+2\times2+\cdots+99\times99\right)+2\times\left(1+2+\cdots+99\right)\)

\(=\frac{99\times\left(99+1\right)\times\left(2\times99+1\right)}{6}+2\times\frac{99\times100}{2}\)

\(=\frac{99\times100\times199}{6}+99\times100=33\times50\times199+99\times100\)

\(=33\times50\times\left(199+3\times2\right)=33\times50\times205=338250\)

b: \(\frac89\times\frac{15}{16}\times\ldots\times\frac{2499}{2500}\)

\(=\left(1-\frac19\right)\times\left(1-\frac{1}{16}\right)\times\ldots\times\left(1-\frac{1}{2500}\right)\)

\(=\left(1-\frac13\right)\times\left(1-\frac14\right)\times\ldots\times\left(1-\frac{1}{50}\right)\times\left(1+\frac13\right)\times\left(1+\frac14\right)\times\ldots\times\left(1+\frac{1}{50}\right)\)

\(=\frac23\times\frac34\times\ldots\times\frac{49}{50}\times\frac43\times\frac54\times\ldots\times\frac{51}{50}=\frac{2}{50}\times\frac{51}{3}=\frac{17}{25}\)

\(K=\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{25}\right)x\left(1-\frac{1}{36}\right)\)

\(K=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x\frac{35}{36}\)

tự rút gọn

thôi tui làm nốt cho

...

\(K=\frac{1x3}{2x2}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x\frac{4x6}{5x5}x\frac{5x7}{6x6}\)

\(K=\frac{7}{2}\)