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A=9+99+999+...+999...9[có 20 chữ số 9]
=10-1+100-1+1000-1+...+1000...0[có 20 chữ số 0]-1
=10+100+1000+...+1000...0[có 20 chữ số 0]+(-1-1-1-1-...-1) [20 chữ số 1]
=10+102+103+...+1020-20
Đặt B=10+102+103+...+1020
=>10B=102+103+...+1021
=>10B-B=102+103+...+1021-10-102-103-...-1020
=>9B=1021-10
=>B=\(\frac{10^{21}-10}{9}\)
=>A=\(\frac{10^{21}-10}{9}-20\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bn tham khảo link này nha
https://olm.vn/hoi-dap/detail/10192559186.html
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999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
A = 9 + 99 + 999 + ... + 999..99 (2019 chữ số 9)
Tổng tất cả các chữ số của A là:
B = 9 + 9 x 2 + 9 x 3 + 9 x 2019
B = 9 x (1 + 2 + 3+ ... + 2019)
B = 9 x (2019 + 1)x[(2019 - 1) : 1 + 1] : 2
B = 18352710
![](https://rs.olm.vn/images/avt/0.png?1311)
9 + 99 + 999.... + 999...9
= 10 - 1 + 100 - 1 + ... + 100...0 - 1 ( 100...0 có 100 chữ số 0 )
= 10 + 100 + 1000 + ... + 100...0 - 1 - 1 - 1 - 1 - ... -1 ( 100...0 có 100 chữ số 0 ) ( 1 - 1 - 1 - 1 - ... -1 có 100 số 1 )
= 111...110 - 100 ( 111...110 có 100 chữ số 1 )
= 111...010
**** cho mình nha
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\(A=\left(10^2-1\right)+\left(10^3-1\right)+...+\left(10^{51}-1\right)\)
\(=-50+\left(10^2+10^3+...+10^{51}\right)\)
\(=-50+\frac{10^{52}-10^2}{10-1}=\frac{10^{52}-10^2}{9}-50\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=111...1090
18 chu so 1