\(\frac{3}{1}+\frac{3}{1+2}+\frac{3}{1+2+3}+...+\frac{3}{1+2+...+100}\)

\(=3\left(\frac{1}{\frac{1\cdot2}{2}}+\frac{1}{\frac{2\cdot3}{2}}+\frac{1}{\frac{3\cdot4}{2}}+...+\frac{1}{\frac{100\cdot101}{2}}\right)\)

\(=3\left(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+...+\frac{2}{100\cdot101}\right)\)

\(=6\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{100\cdot101}\right)\)

\(=6\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\right)\)

\(=6\left(1-\frac{1}{101}\right)=6-\frac{6}{101}=\frac{606-6}{101}=\frac{600}{101}\)

14

Ta có : 1+1+(2+2)+(3+3)

= 2+ 4 + 6

=2+(4+6)

=2+10

=12

à nhầm 12 nhé

A= 1+2+2²+2³+2⁴ / 1+2+2²+2³=2⁰+....+2⁴/ 2⁰+....+2³

=>rút gọn vế trái và vế phải ta được kết quả là ;2⁴=16

B thì làm tương tự bài trên

chúc bạn họ tốt !

\(A=\frac{\left(1+2+2^2+2^3+2^4\right)}{\left(1+2+2^2+2^3\right)}\)

\(A=\frac{2^4\left(1+2+2^2+2^3\right)}{\left(1+2+2^2+2^3\right)}\)

\(A=2^4=16\)

\(B=\frac{\left(1+3+3^2+3^3+3^4\right)}{\left(1+3+3^2+3^3\right)}\)

\(B=\frac{3^4\left(1+3+3^2+3^3\right)}{\left(1+3+3^2+3^3\right)}\)

\(B=3^4=81\)

\(\text{Ta co }A=16< B=81\)

\(\Rightarrow A< B\)

Ta có:

A = \(\frac{1+2+2^2+2^3+2^4}{1+2+2^2+2^3}=\frac{\left(1+2+2^2+2^3\right)+2^4}{1+2+2^2+2^3}\)

  = \(1+\frac{2^4}{1+2+2^2+2^3}=1+\frac{\left(1+2+2^2+2^3\right)+1}{1+2+2^2+2^3}\)

 = \(1+1+\frac{1}{1+2+2^2+2^3}=2+\frac{1}{1+2+2^2+2^3}\)

B = \(\frac{1+3+3^2+3^3+3^4}{1+3+3^2+3^3}=\frac{\left(1+3+3^2+3^3\right)+3^4}{1+3+3^2+3^3}\)

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

 = \(1+2+\frac{1}{1+3+3^2+3^3}=3+\frac{1}{1+3+3^2+3^3}\)

Ta thấy : 2 < 3 => \(2+\frac{1}{1+2+2^2+2^3}< 3+\frac{1}{1+3+3^2+3^3}\)

=> A < B

24877,731 đấy

a ) 13/20

B)

C..........................................................

minh dang tính

lấy máy tính mà bấm

trả lời kiểu gì vậy hả bạn lê thế trung

Tính P = Chúc bạn học tốt nhé

P=1+1/3+1/6+1/10+…..+1/2021×2022÷2

P/2=1/2+1/6+1/12+1/20+…..+1/2021×2022

P/2=1/1×2+1/2×3+1/3×4+…….+1/2021×2022

P/2=1-1/2+1/2-1/3+1/3-1/4+….+1/2021-1/2022=1-1/2022=2021/2022

P=2021/1011

Chúc bn học tốt

a/3 + 9 : 3

= 3 + 3

= 6

b/ =\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+ 2 + 3 + 4

= \(\frac{13}{12}\)+ 9

= \(\frac{121}{12}\)

3 cộng 9:3=6 và 121/12 phải ko bạn

\(3+9:3=3+3=6\)

\(\frac{1}{2}+\frac{1}{3}_{ }+\frac{1}{4}+\frac{2}{1}+\frac{3}{1}+\frac{4}{1}\)\(=\frac{5}{6}+\frac{9}{4}+\frac{7}{1}\)\(=\frac{74}{24}+7\)\(=\frac{74}{24}+\frac{28}{24}\)\(=\frac{102}{24}=\frac{17}{4}\)

NHANH LÊN MIK ĐANG CẦN GẤP NHA CÁC BAN

\(\frac{1}{6}\)(2x-3) = \(\frac{-1}{2}\)(x-\(\frac{1}{4}\))-\(\frac{2}{3}\)
\(\frac{1}{3}\)x - \(\frac{1}{2}\)=\(\frac{-1x}{2}\)-\(\frac{-1}{8}\)-\(\frac{2}{3}\)
\(\frac{1x}{3}\)-\(\frac{1}{2}\)=\(\frac{-1x}{2}\) - \(\frac{19}{24}\)
\(\frac{1x}{3}\) - \(\frac{1}{2}\) - \(\frac{-1x}{2}\) - \(\frac{19}{24}\) =0
\(\frac{5x}{6}\) - \(\frac{7}{24}\)=0
\(\frac{5x}{6}\) = \(\frac{7}{24}\)
x = \(\frac{7}{20}\)

đáp số 100

= (11+19)+(12+18)+(13+17)+(14+16)+15

=(30+30+30+30)+15

=120+15

=135

= (11+19)+(12+18)+(13+17)+(14+16)+15

=(30+30+30+30)+15

=120+15

=135

nhanh đi bà con hàng xóm

nhanh đi bớ người ta

Đặt A = 1/3 + 2/3² + 3/3³ + 4/3^4 + ... + 100/3^100

=> 3A= 1 + 2/3 + 3/3² + 4/3³ + .... + 100/3^99

=> 3A-A = 1 + (2/3 - 1/3) + (3/3² - 2/3²) +...+ (100/3^99 - 99/3^99) - 100/3^100

=> 2A= 1+ 1/3 + 1/3² + 1/3³ +...+ 1/3^99 - 100/3^100

Đặt B = 1/3 + 1/3² + 1/3³ +...+ 1/3^99

=> 3B = 1 + 1/3 + 1/3² + 1/3³ +...+ 1/3^98

=> 2B = 1 - 1/3^99 => B = (1 - 1/3^99)/2

Thay vào 2A => 2A= 1+ 1/2 - 1/(2x3^99) - 100/3^100 < 1+ 1/2 = 3/2

=> A < 3/4