1)

\(A=\dfrac{1}{5}+\dfrac{2}{5^2}+\dfrac{3}{5^3}+...+\dfrac{500}{5^{500}}\\ 5A=1+\dfrac{2}{5}+\dfrac{3}{5^2}+...+\dfrac{500}{5^{49}}\\ 5A-A=\left(1+\dfrac{2}{5}+\dfrac{3}{5^2}+...+\dfrac{500}{5^{49}}\right)-\left(\dfrac{1}{5}+\dfrac{2}{5^2}+\dfrac{3}{5^3}+...+\dfrac{500}{5^{500}}\right)\\ 4A=1-\dfrac{500}{5^{500}}\\ A=\left(1-\dfrac{500}{5^{500}}\right):4\\ A=1:4-\dfrac{500}{5^{500}}:4\\ A=\dfrac{1}{4}-\dfrac{500}{5^{500}\cdot4}< \dfrac{1}{4}< \dfrac{5}{16}\)

Vậy \(A< \dfrac{5}{16}\)

\(A=1+2+2^2+2^3+\ldots+2^{500}\)

\(2A=2\times(1+2+2^2+2^3+\ldots+2^{500}\)

\(2A=2+2^2+2^3+2^4+\ldots+2^{501}\)

\(2A-A=(2+2^2+2^3+2^4+...+2^{501})-(1+2+2^2+2^3+\ldots+2^{500)}\)

\(A=2^{501}-1\)

đặt A= 1+2+2^2+2^3+...+2^500

=>2A=2+2²+2³+...+2⁵⁰¹

=>2A-A=2+2²+2³+...+2⁵⁰⁰+2⁵⁰¹-(1+2+2²+2³+...+2⁵⁰⁰)

=> A=2+2²+2³+...+2⁵⁰⁰+2⁵⁰¹-1-2-2²-2³-...-2⁵⁰⁰

=2⁵⁰¹-1

mik ko chắc là đúng đâu bn

1-1/2+1/3-1/4+......-1/1000 

=(1+1/3+1/5+......+1/999)-(1/2+1/4+.......+1/1000) 

=(1+1/2+1/3+1/4+.....+1/1000)-2(1/2+1/4+.......+1/1000) 

=(1+1/2+1/3+.........+1/1000)-(1+1/2+.....+1/500) 

=1/501 +1/502+1/503+.....+1/1000 ; 

mat khác: 

500-500/501-501/502-.....-999/1000 

=(1-500/501)+(1-501/502)+.....+(1-999/1000)=1/501+1/502+....+1/1000  

=>D=1

\(\dfrac{1}{500}+\dfrac{3}{500}+\dfrac{5}{500}+...+\dfrac{95}{500}+\dfrac{97}{500}+\dfrac{99}{500}\)

\(=\left(\dfrac{1}{500}+\dfrac{99}{500}\right)+\left(\dfrac{3}{500}+\dfrac{97}{500}\right)+\left(\dfrac{5}{500}+\dfrac{95}{500}\right)+...\)

\(=\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+...\) ( 50 số )

\(=\dfrac{1}{5}.50\)

\(=10\)

Nguyễn Huy TúAce Legonasoyeon_Tiểubàng giảiTrần Việt Linh

Võ Đông Anh TuấnHoàng Lê Bảo NgọcPhương An

lầy dạ??

99

bài này mik làm rồi

mik bảo đảm đo 

tick mik thật nhiều nhé các bạn

\(A=5\)

Dựa vào câu hỏi trên ta có dãy số 1+3+7+...........................+97+99

lười thế

1

2⁵⁰⁰ và 3³⁰⁰

2⁵⁰⁰= (2⁵)¹⁰⁰= 32¹⁰⁰

3³⁰⁰= (3³)¹⁰⁰= 27¹⁰⁰

Vì 32¹⁰⁰> 27¹⁰⁰ nên 2⁵⁰⁰ > 3³⁰⁰

Vậy...

a)

4 . 25 – 12 . 25 + 170 : 10 

= (4 . 25) – (12 . 25) + (170 : 10) 

= 100 - 300 + 17 

= -183

b)

(7 + 33 + 32) . 4 – 3 

= (7 + 27 + 9) .4 – 3

= 43 . 4 – 3

= (43 . 4) – 3

= 45

c)

12 : {400 : [500 – (125 + 25 . 7)}

= 12 : {400 : [500 – (125 + 175)}

= 12 : (400: 200)

= 12 : 2

= 6

d)

168 + {[2.(2⁴ + 3²) - 256⁰] : 72}.

= 168 + [2 . (16 + 9) – 1] : 49

= 168 + 49: 49

= 168 + 1 

= 167

a) 

4 . 25 – 12 . 25 + 170 : 10 

= (4 . 25) – (12 . 25) + (170 : 10) 

= 100 - 300 + 17 

= -183

b)

(7 + 33 + 32) . 4 – 3 

= (7 + 27 + 9) .4 – 3

= 43 . 4 – 3

= (43 . 4) – 3

= 45

c)

12 : {400 : [500 – (125 + 25 . 7)}

= 12 : {400 : [500 – (125 + 175)}

= 12 : (400: 200)

= 12 : 2

= 6

d)

168 + {[2.(2⁴ + 3²) - 256⁰] : 72}.

= 168 + [2 . (16 + 9) – 1] : 49

= 168 + 49: 49

= 168 + 1 

= 167

\(24:\left\{390-[500-\left(125+35.7\right)]\right\}=2^x\)

\(24:\left\{390-[500-\left(125+245\right)]\right\}=2^x\)

\(24:\left\{390-[500-370]\right\}=2^x\)

\(24:\left\{390-130\right\}=2^x\)

\(24:260=2^x\)

Chỗ này sai đề ạ !

24 : { 390 - [ 500 - ( 125 + 35 . 7 ) ] } = 2^x

2^x = 24 : { 390 - [ 500 - ( 125 + 245 ) ] }

2^x = 24 : { 390 - [ 500 - 370 ] }

2^x = 24 : { 390 - 130 }

2^x = 24 : 260

2^x = 6/65 = ......................

=> Đề sai