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P
1
13 tháng 8 2016
\(A=4+4^2+4^3+...+4^{100}\)
\(A=\left(4+\text{ }4^2\right)+\left(4^3+4^4\right)+...+\left(4^{99}+4^{100}\right)\)
\(A=\left(1+4\right).\left(4\right)+\left(1+4\right).\left(4^3\right)+...+\left(1+4\right).\left(4^{99}\right)\)
\(A=5.\left(4+4^3+4^5+...+4^{99}\right)\)
Vậy A chia hết cho 5
Các bạn nha!
NN
3
15 tháng 1 2020
A=2+22+23+....+299+2100
A=(2+22+23+24+25)+(26+27+28+29+210)+......+(296+297+298+299+2100)
A=(2+22+23+24+25)+25.(2+22+23+24+25)+....+295.(2+22+23+24+25)
A=62+25.62+.....+295.62
A=62.(1+25+.....+295)
A=31.2.(1+25+...+295)\(⋮\)31
Vậy A\(⋮\)31
Chúc bn học tốt
P
3
27 tháng 12 2017
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28 tháng 12 2017
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NP
2
13 tháng 7 2017
Ta có: A= 2+2^2+2^3+2^4+...+2^100=
= (2+2^2)+(2^3+2^4)+...+(2^99+2^100)=6+2^2.(2+2^2)+...+2^98.(2+2^2)=
= 6+2^2.6+...+2^98.6=6.(1+2^2+...+2^98)
Vì 6\(⋮\)6 nên 6.(1+2^2+...+2^98)\(⋮\)6 hay A\(⋮\)6.
\(A=\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{98}\left(2+2^2\right)\\ A=\left(2+2^2\right)\left(1+2^2+...+2^{98}\right)=6\left(1+2^2+...+2^{98}\right)⋮6\)
A=2+22+23+24+....+2100A=2+22+23+24+....+2100
A=(2+22)+(23+24)+....+(299+2100)A=(2+22)+(23+24)+....+(299+2100)
A=1.(2+22)+22.(2+22)+....+298.(2+22)A=1.(2+22)+22.(2+22)+....+298.(2+22)
A=(2+22).(1+22+....+298)A=(2+22).(1+22+....+298)
A=6.(1+22+....+2