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F = 7 + 72 + 73 + 74 + ..... + 7100
F= 7+(1+7)+73+(1+7)+...+799+(1+7)
F = 7x8+73x8+...+799x8
F= 8x(7+73+...+799)
mà 8 chia hết 8 => 8(7+73+...+799) chia hết 8
Vậy F chia hết cho 8
a)\(...A=\dfrac{2^{50+1}-1}{2-1}=2^{51}-1\)
b) \(...\Rightarrow B=\dfrac{3^{80+1}-1}{3-1}=\dfrac{3^{81}-1}{2}\)
c) \(...\Rightarrow C+1=1+4+4^2+4^3+...+4^{49}\)
\(\Rightarrow C+1=\dfrac{4^{49+1}-1}{4-1}=\dfrac{4^{50}-1}{3}\)
\(\Rightarrow C=\dfrac{4^{50}-1}{3}-1=\dfrac{4^{50}-4}{3}=\dfrac{4\left(4^{49}-1\right)}{3}\)
Tương tự câu d,e,f bạn tự làm nhé
a) 310 . 315 : 322 + 47 : 44
= 3(10 + 15 - 22 ) + 4(7-4)
= 33 + 43
= ( 3.4)3
=123
b)[ (52 . 53 ) - 72 . 2 ) : 2 ] . 6 = 7 . 25
[ (52 . 53 ) - 72 . 2 ) : 2 ] . 6 = 7 . 32
= 224
Bài 1:
\(a,A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\\ A=\left(1+2\right)\left(2+2^3+...+2^{2009}\right)=3\left(2+...+2^{2009}\right)⋮3\\ A=\left(2+2^2+2^3\right)+...+\left(2^{2008}+2^{2009}+2^{2010}\right)\\ A=\left(1+2+2^2\right)\left(2+...+2^{2008}\right)=7\left(2+...+2^{2008}\right)⋮7\)
\(b,\left(\text{sửa lại đề}\right)B=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{2009}+3^{2010}\right)\\ B=\left(1+3\right)\left(3+3^3+...+3^{2009}\right)=4\left(3+3^3+...+3^{2009}\right)⋮4\\ B=\left(3+3^2+3^3\right)+...+\left(3^{2008}+3^{2009}+3^{2010}\right)\\ B=\left(1+3+3^2\right)\left(3+...+3^{2008}\right)=13\left(3+...+3^{2008}\right)⋮13\)
Bài 2:
\(a,\Rightarrow2A=2+2^2+...+2^{2012}\\ \Rightarrow2A-A=2+2^2+...+2^{2012}-1-2-2^2-...-2^{2011}\\ \Rightarrow A=2^{2012}-1>2^{2011}-1=B\\ b,A=\left(2020-1\right)\left(2020+1\right)=2020^2-2020+2020-1=2020^2-1< B\)
Câu 1 :
\(A=5+5^2+5^3+......+5^{2016}\)( 1 )
\(A.5=5^2+5^3+5^4+.....+5^{2017}\)( 2 )
Lấy ( 2 ) - ( 1 ) ta được :
\(A.5-A=\left(5^2+5^3+5^4+......+5^{2017}\right)-\left(5+5^2+5^3+......+5^{2016}\right)\)
\(A.4=5^{2017}-5\)
\(A=\left(5^{2017}-5\right):4\)
\(\Rightarrow4A+5=\left(5^{2017}-5\right):4.4\)
\(\Rightarrow4A+5=5^{2017}-5\)
Câu 2 :
\(A=7+7^2+7^3+.....+7^{2016}\)( 1 )
\(A.7=7^2+7^3+7^4+......+7^{2017}\)( 2 )
Lấy ( 2 ) - ( 1 ) ta được :
\(A.7-A=\left(7^2+7^3+7^4+.....+7^{2017}\right)-\left(7+7^2+7^3+.....+7^{2016}\right)\)
\(A.6=7^{2017}-7\)
\(A=\left(7^{2017}-7\right):6\)
\(\Rightarrow6.A+7=\left(7^{2017}-7\right):6.6\)
\(\Rightarrow6.A+7=7^{2017}-7\)
Câu 1:
\(A=5+5^2+5^3+......+5^{2016}\)
\(5A=5^2+5^3+5^4+.......+5^{2017}\)
\(\Rightarrow5A-A=\left(5^2+5^3+5^4+.......+5^{2017}\right)-\left(5+5^2+5^3+.......+5^{2016}\right)\)
\(\Rightarrow5A-A=5^2+5^3+5^4+.........+5^{2017}-5-5^2-5^3-........-5^{2016}\)
\(\Rightarrow4A=5^{2017}-5\)
\(\Rightarrow4A+5=5^{2017}\)
Câu 2 tương tự câu 1