\(S=1+2+2^2+2^3+...+2^9\) 

Đặt \(2S=2+2^2+2^3+2^4+...+2^{10}\) 

\(2S-S=2^{10}-1\) hay \(S=2^{10}-1< 2^{10}\)

\(\Rightarrow\) \(2^{10}=2^2.2^8< 5.2^8\) 

Vậy \(S< 5.2^8\)

\(#Tuyết\)

2S=2+2^2+...+2^10

=>S=2^10-1=1023

5*2^8=256*5=1280

=>S<5*2^8

`@` `\text {Answer}`

`\downarrow`

`S = 1 + 2 + 2^2 + 2^3 + ... + 2^9`

`=> 2S = 2 + 2^2 + 2^3 + ... + 2^10`

`=> 2S - S = (2+2^2 + 2^3 + ... + 2^10) - (1 + 2 + 2^2 + 2^3+...+2^9)`

`=> S = 2^10 - 1`

Mà `2^10 - 1 < 2^10`

`=> S < 2^10 (1)`

Ta có:

 `2^10 = 2^7*8`

Mà `5*2^8 = 5* 2 * 2^7 = 10* 2^7`

Vì `10 > 8 => 2^7 * 8 < 2^7  * 10 (2)`

Từ `(1)` và `(2)`

`=> S < 5 * 2^7``.`

A = 99 x2 + 33+333+3333+...+333...33 (100 chữ số 3) 

đặt B = 33+333+3333+...+3333....33 = (99+999+9999+....+999...99): 3

= (10²-1+10³-1+10⁴-1+....+ 10¹⁰⁰-1):3

=  (10²+10³+10⁴+....+ 10¹⁰⁰-99):3

đặt  C= 10²+10³+10⁴+....+ 10¹⁰⁰

Cx 10 = 10³+10⁴+....+ 10¹⁰⁰+10¹⁰¹

^{Suy ra C x9 =} 10¹⁰¹- 10²

^{Bạn tính tiếp nhé.}

35+335+3335+....+333...35(có 100 c/s 3)

=35+35+3x100+35+3x1100+....+3x111...00(99 c/s 1)+35

=35x100+3x(100+1100+...+111....100(99 c/s 1))

=3500+3x(1.100+11.10+....+111...1(99 c/s 1).10)

=3500+3 x ((1+11+..+111...1(99 c/s 1))x100)

Chịu thôi , đến đoạn này tớ bí !!!

Sorry nha!

A = 1 . 3 . 5 - 3. 5 . 7 + 5 . 7 . 9 - 7.9.11 + ... + 97.99.101

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + … + 98.99.100.4
= 1.2.3.4 + 2.3.4(5 - 1) + 3.4.5(6 - 2) + … + 98.99.100(101 - 97)
= 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + … + 98.99.100.101 - 97.98.99.100
= 98.99.100.101
=> A = 98.99.25.101
A = 24 497 550

mk ko viết đề nhé

C=1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

C= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)

C= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99

C= 15 + 95.97.99.101

=>C=\frac{15 + 95.97.99.101}{8}

1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)

= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99

=15 + 95.97.99.101

=> A = \frac{15.95 + 97.99.101}{8}