\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)

\(A=\frac{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}{\left(2.3.4.....100\right).\left(2.3.4.....100\right)}\)

\(A=\frac{1.101}{2.100}=\frac{101}{200}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)

\(A=\frac{1.2.3.4.....99}{2.3.4.5.....100}.\frac{3.4.5.6.....101}{2.3.4.5.....100}\)

\(A=\frac{1}{100}.\frac{101}{2}\)

\(A=\frac{101}{200}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{99.101}{100.100}\)

\(A=\frac{1.2...99}{2.3...100}.\frac{3.5...101}{2.3...100}\)

\(A=\frac{1}{100}.\frac{101}{2}\)

\(=\frac{101}{200}\)

\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)

\(B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)

\(B=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}....\frac{1558}{1560}\)

\(B=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{38.41}{39.40}\)

\(B=\frac{1.2.3...38}{2.3...39}.\frac{4.5...41}{3.4...40}\)

\(B=\frac{1}{39}.\frac{41}{3}\)

\(B=\frac{41}{117}\)

Bài 1

a) 15 + 4.12 - 3²

=15 + 48 - 9

= 63 - 9

= 54

b) {[(37 + 13) : 5].2 - 45 : 5}.7 - 2022⁰

= [(50 : 5).2 - 9].7 - 1

= (10.2 - 9).7 - 1

= (20 - 9).7 - 1

= 11.7 - 1

= 77 - 1

= 76

Bài 2

a) 13x + 3 = 16

13x = 16 - 3

13x = 13

x = 13 : 13

x = 1

b) 2x - 138 = 2⁴ : 2³

2x = 2 + 138

2x = 140

x = 140 : 2

x = 70

\(\frac{-1}{3}:\frac{-5}{6}=\frac{-1}{3}\times\frac{-6}{5}=\frac{2}{5}\)

@muối

(-1/3) : (-5/6) = 2/5

\(\frac{-1}{3}:\frac{-5}{6}\)

\(=\frac{-1}{3}.\frac{6}{-5}\)

\(=\frac{-6}{-15}\)

\(=\frac{-2}{-5}\)

\(=\frac{2}{5}\)

a: Ta có: \(\dfrac{4}{\sqrt{7}-\sqrt{3}}+\dfrac{6}{3+\sqrt{3}}+\dfrac{\sqrt{7}-7}{\sqrt{7}-1}\)

\(=\sqrt{7}+\sqrt{3}+3-\sqrt{3}-\sqrt{7}\)

=3

25%−112+0,5⋅125=14−32+12⋅125=−54+65=−120

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}\)

\(\text{=}\dfrac{-1}{15}+\dfrac{1}{5}+\dfrac{2}{45}\)

\(\text{=}\dfrac{8}{45}\)

Áp dụng tính chất đổi dấu và giao hoán của phép nhân phân số, ta có:

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}=\dfrac{1}{5}.\dfrac{-3}{9}+\dfrac{1}{5}.\dfrac{4}{4}+\dfrac{1}{5}.\dfrac{2}{9}\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+1+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+\dfrac{9}{9}+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}.\dfrac{8}{9}\)

                                           \(=\dfrac{8}{45}\)

Ta thấy tổng: 2 + 4 + 6 + 8 + ... + 100 + 102 là tổng của các số chẵn => tổng này chẵn nên chia cho 3 vẫn là số chẵn vì 3 là số lẻ, khác 815

=> kết quả sai

\(\text{Kq sai rùi}\)
 

Tớ chắc chắn là sai vì 815 không chia hết cho 3