Tính: \(T=9^9+9^{99}+9^{999}+9^{9999}+9^{99999}+9^{999999}+........+9^{9999999999}+9^{9999999999}+9^{999999999999}+9^{999999999999}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
9 . 1 + 9. 11 + 9.111 + 9.1111 + 9.11111 + 9.111111 + 9.1111111 + 9.11111111 + 9.111111111 + 9.1111111111
![](https://rs.olm.vn/images/avt/0.png?1311)
= (10-1) + (100 -1) + (1000-1) + (10000-1) + ............+ (10000000000-1)
= ( 10+100+1000+10000+..........+10000000000) - (1+1+1+1+..........+1+1)
=11111111110 - 1.10
=1111111100
= (10-1) + (100 -1) + (1000-1) + (10000-1) + ............+ (10000000000-1)
= ( 10+100+1000+10000+..........+10000000000) - (1+1+1+1+..........+1+1)
=11111111110 - 1.10
=1111111100
![](https://rs.olm.vn/images/avt/0.png?1311)
T + n = 10 + 100 + 1000 + 10000 + ... + 10000...0000 ( n chữ số 0 )
T + n = 10^1 + 10^2 + 10^3 + ... + 10^n
10 ( T + n ) = 10^2 + 10^3 + 10^4 + ... + 10^n+1
9 ( T + n ) = ( 10^2 + 10^3 + 10^4 + ... + 10^n + 1 ) - ( 10^1 + 10^2 + 10^3 + ... + 10^n )
9 ( T + n ) = 10^n+1 - 10^1 = 10^n+1 - 10
9 T + 9n = 10^n+1 - 10
9 T = 10^n+1 - 10 - 9n = 9999....9990 ( n - 1 chữ số 9 và 1 chữ số 0 ) - 9n
T = 9999...9990 ( n - 1 chữ số 9 và 1 chữ số 0 ) - 9n / 9 = 1111...1110 - n
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 9 +99 +999 + 9999 + 99999+ 999999 + 9999999 + 99999999 + 999999999 + 9999999999 = 11111111100
Đáp số : 11111111100
![](https://rs.olm.vn/images/avt/0.png?1311)
=9(1+11+111+1111+....+11111111)
=9.12345678
kết quả ghi re chẳng đc j nên để thế này cho gọn
#Học-tốt
- Đặt \(A=9+99+999+9999+99999+...+99999999\)
- Ta có: \(A=9+99+999+9999+99999+...+99999999\)
\(\Leftrightarrow A=9.\left(1+11+111+1111+11111+...+11111111\right)\)
\(\Leftrightarrow A=9.12345678\)
\(\Leftrightarrow A=111111102\)
Vậy \(A=111111102\)
!!@#!@ ^_^ Bn hok tốt nha ^_^ $!@#@!#
![](https://rs.olm.vn/images/avt/0.png?1311)
9 + 99 + 999 + .....+ 9999999999.......9999999(có 100 c/s 9)
=10-1+102-1+103-1+...+10100-1
=10+102+103+..+10100+(-1-1-1-...-1(100 chữ số 1))
=10+102+103+...+10100-100
Đặt : A=10+102+103+...+10100
=>10A=102+103+...+10101
=>10A-A=102+103+...+10101-10-102-103-...-10100
=>9A=10101-10
=>A=\(\frac{10^{101}-10}{9}\)
suy ra: 9 + 99 + 999 + .....+ 9999999999.......9999999(có 100 c/s 9)
=\(\frac{10^{101}-10}{9}-10^2-\frac{10^{101}-10}{9}-100\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta co:A=9+9+999+..........+9999999999
A=10-1+100-1+1000-1+...........+10000000000-1(10 so 0)
A=(10+100+1000+...+10000000000)-(1+...+1)
A=(1+10+100+1000+........+10000000000)-(1+1+........+1)
A=11111111111-11
A=11111111100
![](https://rs.olm.vn/images/avt/0.png?1311)