\(A=3+3^2+3^3+3^4+.....+3^{25}+3^{26}\)
\(\Rightarrow A+1=1+3+3^2+3^3+3^4+....+3^{25}+3^{26}\)
\(\Rightarrow A+1=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+.....+\left(3^{24}+3^{25}+3^{26}\right)\)
\(A+1=40+3^3\left(1+3+3^2\right)+....+3^{24}\left(1+3+3^2\right)\)
\(A+1=40+3^3\cdot40+....+3^{24}\cdot40\)
\(A+1=40\left(1+3^3+...+3^{24}\right)\)
\(\Rightarrow\left(A+1\right)⋮40\)
\(\Rightarrow A:40\)dư 39
A= 3+3^2+3^3+...+3^25 (25 SH)
=3^2+(3+3^3)+(3^4+3^6)+...+(3^23+3^25)
=9+40.1+3^3.(3+3^3)+...+3^22.(3+3^3)
=9+40.1+3^3.40+...+3^22.40
=9+40.(1+3^3+...+3^22) chia 40 dư 9
(1+3^3+....+3^22 thuộc N ; 40 chia hết cho 40 nhưng 9 không chia hết cho 40)
Vậy Achia 40 dư 9
nhớ k đúng nhe!
A = 3 + 32 + 33 +34 + ... + 325
A = 31+2+3+4+...+25 = 3 . 325 = 975
975 : 40 = 24 dư 15
Vậy A : 40 dư 15
