\(A=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)

a, Ta có : 2²⁰¹³ = (2³)⁶⁷¹ = 8⁶⁷¹

3¹³⁴⁴ = (3²)⁶⁷² = 9⁶⁷²

Mà 8⁶⁷¹ < 9⁶⁷² 

Vậy 2²⁰¹³ < 3¹³⁴⁴

b, \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{64\cdot69}\)

\(A\cdot5=\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

\(A=\frac{65}{276}\div5=\frac{13}{276}\)

a, Ta có: 2²⁰¹³ = (2³)⁶⁷¹ = 8⁶⁷¹

3¹³⁴⁴ = (3²)⁶⁷² = 9⁶⁷²

Vì 8⁶⁷¹ < 9⁶⁷² => 2²⁰¹³ < 3¹³⁴⁴

b, A = \(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

5A = \(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)

5A = \(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{64}-\frac{1}{69}\)

5A = \(\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

A = \(\frac{65}{276}:5=\frac{13}{276}\)

5B=\(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

5B=\(\frac{9-4}{4\cdot9}+\frac{14-9}{9\cdot14}+...+\frac{69-64}{64.69}\)

5B=\(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

5B=\(\frac{65}{276}\)

B=\(\frac{13}{276}\)

\(B=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)

\(\Rightarrow5B=\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{64.69}\)

\(5B=\frac{9-4}{4.9}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(5B=\frac{65}{276}\)

\(B=\frac{65}{276}:5\)

\(B=\frac{13}{276}\)

\(B=\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

\(5B=\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}+...+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(5B=\frac{65}{276}\)

\(B=\frac{65}{276}:5\)

\(B=\frac{13}{276}\)

a 2^2015>3^1029

b 5A=\(\frac{5}{4.9}\)+\(\frac{5}{9.14}\)+\(\frac{5}{14.19}\)+.....+\(\frac{5}{64.69}\)

 5A=1/4-1/9+1/9-1/14+1/14-1/19+1/19+....+1/64-1/69

5A=1/4-1/9

A=(1/4-1/9)/5

A=1/36

kho lam bo tay

khó lắm bạn ơi

b: Ta có: \(B=\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{64\cdot69}\)

\(=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{65}{4\cdot69}\)

\(=\dfrac{13}{276}\)

\(A=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+...+\dfrac{2}{97\cdot100}\\ A=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{97\cdot100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{100}\right)=\dfrac{2}{3}\cdot\dfrac{99}{100}=\dfrac{33}{50}\\ B=\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{64\cdot69}\\ B=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{69}\right)=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)

\(C=70\left(\dfrac{13}{56}+\dfrac{13}{72}+\dfrac{13}{90}\right)=70\cdot13\left(\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\\ C=910\left(\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{10}\right)=910\cdot\dfrac{3}{70}=39\)

\(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}\)

\(=\frac{1}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{44.49}\right)\)

\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\right)\)

\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)=\frac{9}{196}\)

thực hiện phép tính:1-3-5-...-49/89

ko biết làm

đặt A = 1/4.9 + 1/9.14+ 1/14.19 + .....1/44.49

ta có 5.A = 5/4.9 + 5/9.14+ 5/14.19 + .....5/44.49 = 1/4- 1//9 + 1/9 - 1/14+........+ 1/44 -1/49 = 1/4 - 149 = 45/196

suy ra A = 9/196

đặt B = 1-3--5-...-49 = 1 - (3+5+ ....+ 49)

đặt C = 3+5+...+49        khoảng cách là d = 2

số các số hạng là (49-3)/2 + 1 = 24

tổng C = (49+3)/2 x 24 = 624

suy ra B = 1-624 = -623

vậy A = 9/196 .(-623)/89 = -9/28

-9/28

giúp tớ nhé 

tớ bị trù 690 điểm 

cảm ơn nhé 

1-1/64.69=6369/6469