Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 3 :
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{99\times100}\)
Ta có : \(\frac{1}{1\times2}=\frac{2-1}{1\times2}=\frac{2}{1\times2}-\frac{1}{1\times2}=1-\frac{1}{2}\)
\(\frac{1}{2\times3}=\frac{3-2}{2\times3}=\frac{3}{2\times3}-\frac{2}{2\times3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{99\times100}=\frac{100-99}{99\times100}=\frac{100}{99\times100}-\frac{99}{99\times100}=\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10\times11}+\frac{1}{11\times12}+...+\frac{1}{38\times39}\)
Ta có : \(\frac{1}{10\times11}=\frac{11-10}{10\times11}=\frac{11}{10\times11}-\frac{10}{10\times11}=\frac{1}{10}-\frac{1}{11}\)
\(\frac{1}{11\times12}=\frac{12-11}{11\times12}=\frac{12}{11\times12}-\frac{11}{11\times12}=\frac{1}{11}-\frac{1}{12}\)
\(\frac{1}{38\times39}=\frac{39-38}{38\times39}=\frac{39}{38\times39}-\frac{38}{38\times39}=\frac{1}{38}-\frac{1}{39}\)
\(\frac{1}{39\times40}=\frac{40-39}{39\times40}=\frac{40}{39\times40}-\frac{39}{39\times40}=\frac{1}{39}-\frac{1}{40}\)
\(\Rightarrow B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
3.
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{38.39}+\frac{1}{39.40}\)
\(B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
Câu b
Ta có :x + 3 /1.3 +3/3.5 + 3/5.7+...+3/13.15=2 1/5
X + 2/3.(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15)1=11/5
X+2/3.(1-1/15)=11/5
X+ 2/3.14/15=11/5
X + 28/45=11/5
X = 11/5 -28/45
X=71/45
Câu a gợi ý
1/2-1/3/1/6=0
1/2- 1/3 - 1/6 ) x (1/2 + 2/3 + 3/4 +4/5 + .......+ 2019 /2020 ) =0
3/4:x=9/10
X = 3/4:9/10
X = 5/6
1.
a) 5/8 x 4/10 + 2/3 =
= 1/4+ 2/3 = 11/12
b)5/12 x 4/7+5/12 x3/7
=5/12 x (4/7 +3/7)
=5/12 x1 = 5/12
c)(4/5 + 3/10 - 1/5 ) x 6 : 4/7
= ( 8/10 + 3/10 + 2/10) x 6 x 7/4
=13/10 x 21/2
=273/20
2.
5/8 và 3/2
ta có 5/8 =10/16 ; 3/2 =24 /16
vì 24 /16 >10 /16 nên 3/2 > 5/8
b. tương tự như câu a nha
c 418/417 và 925 /926
418/417 > 1 ; 925 /926 < 1
vì 418 /417 >1 mà 925/926 < 1 nên 418 / 417 > 925 /926
chúc bạn học tốt nha !
a) \(\frac{x}{y}.\frac{3}{7}=\frac{4}{9}\)
\(\frac{x}{y}=\frac{4}{9}:\frac{3}{7}\)
\(\frac{x}{y}=\frac{4}{9}.\frac{7}{3}\)
\(\frac{x}{y}=\frac{28}{27}\)
\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)
=> \(\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)\times x=\frac{28}{15}\)
=> \(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\times x=\frac{28}{15}\)
=> \(\left(\frac{1}{3}-\frac{1}{15}\right)\times x=\frac{28}{15}\)
=> \(\frac{4}{15}\times x=\frac{28}{15}\)
=> \(x=\frac{28}{15}:\frac{4}{15}\)
-> \(x=7\)
\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)
\(a\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)=\frac{28}{15}\)
\(a\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{28}{15}\)
\(a\times\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{28}{15}\)
\(a\times\frac{4}{15}=\frac{28}{15}\)
\(a=\frac{28}{15}:\frac{4}{15}\)
\(a=\frac{28}{15}\times\frac{25}{4}\)
\(a=\frac{28}{4}=7\)
3/4 × 8/9 × 15/16 × ... × 99/100
= 1×3/2×2 × 2×4/3×3 × 3×5/4×4 × ... × 9×11/19×10
= 1×2×3×...×9/2×3×4×...×10 × 3×4×5×...×11/2×3×4×...×10
= 1/10 × 11/2
= 11/20
chỉ cần cách trình bày các bạn có thể làm ví dụ
\(\frac{x}{3}=\frac{16}{24}\Rightarrow x.24=16.3\)
\(\Rightarrow x.24=48\)
\(\Rightarrow x=2\)
\(\frac{x}{4}=\frac{9}{x}\Rightarrow x^2=4.9\)
\(\Rightarrow x^2=36\)
\(\Rightarrow x=\pm6\)
Chúc em học tốt