\(S=\left(4+4^2\right)+\left(4^3+4^4\right)+...+\left(4^{99}+4^{100}\right)\)
\(=4.\left(1+4\right)+4^3.\left(1+4\right)+...+4^{99}.\left(1+4\right)\)
\(=4.5+4^3.5+...+4^{99}.5\)
\(=5.\left(4+4^3+...+4^{99}\right)\text{chia hết cho 5}\left(đpcm\right)\)
S=(4+42)+(43+44+..........+(499+4100)
S=4.(1+4)+43.(1+4)+..........+499.(1+4)
S=4.5+43.5+.......499.5
S=5.(4+43+....+499)
Vậy S chia hết cho 5
Ta có:S=4+42+43+44+........+499+4100
S=(4+42)+(43+44)+..........+(499+4100)
S=(4+4.4)+(43+43.4)+...........+(499+499.4)
S=4.(4+1)+43.(4+1)+...........+499.(4+1)
S=4.5+43.5+..........+499.5
S=(4+43+............+499).5 chia hết cho 5
=>đpcm
=> S = ( 4 + 42 ) + ( 43 + 44 ) + .... + ( 499 + 4100 )
=> A = 4 ( 1 + 4 ) + 43 ( 1 + 4 ) + .... + 499 ( 1 + 4 )
=> A = 4.5 + 43 .5 + ..... + 499 .5
=> A = 5.( 4 + 43 + ..... + 499 )
Vì 5 ⋮ 5 => A ⋮ 5
