Ta có:
\(5+5^2+5^3+5^4+...+5^{10}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^9+5^{10}\right)\)
\(=5.\left(1+5\right)+5^3.\left(1+5\right)+...+5^9.\left(1+5\right)\)
\(=5.6+5^3.6+...+5^9.6\)
\(=6.\left(5+5^3+...+5^9\right)\)
\(\Rightarrow5+5^2+5^3+5^4+...+5^{10}⋮6\)
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5+52+53+54+...+510
(5+52)+(53+54)+...+(59+510)
5.(1+5)+53.(1+5)+...+59.(1+5)
5.6+53.6+...+59.6
6.(5+53+...+59)
vì 6 chia hết cho 6
suy ra 5+52+53+54+...+510 chia hết cho 6 (đpcm)
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