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=7^2003:7^2000+7^2002:7^2000+7^2001:7^2000
=7^3+7^2+7
=343+49+7=399
( 72003 + 72002 ) \(\div\)( 72001 x 7 )
= ( 72003 + 72002 ) \(\div\)( 72001+1)
= ( 72003 + 72002 ) \(\div\)72002
= ( 72003 \(\div\) 72002 ) + ( 72002 \(\div\)72002)
= 72003-2002 + 72002-2002
= 71 + 70
= 7 + 1 = 8
HK TỐT
\(\left(7^{2003}.7^{2002}\right):\left(7^{2001}.7\right)\)
\(=\left(7^{2003}.7^{2002}\right):\left(7^{2001+1}\right)\)
\(=7^{2003}.7^{2002}:7^{2002}=7^{2003}.\left(7^{2002}:7^{2002}\right)\)
\(=7^{2003}.1=7^{2003}\)
\(a,\left(7^{2003}+7^{2002}\right):7^{2001}\)
\(=7^{2003}:7^{2001}+7^{2002}:7^{2001}\)
\(=7^2+7\)
\(=49+7\)
\(=56\)
a, \(\left(7^{2003}+7^{2002}\right)\div7^{2001}=7^{2001}.\left(7^2+7\right)\div7^{2001}=7^2+7=56\)
b, \(\left(5^4+4^7\right)\left(8^9-2^7\right)\left(2^4-4^2\right)\)
\(=\left(5^4+4^7\right)\left(8^9-2^7\right)\left(16-16\right)\)
\(=\left(5^4+4^7\right)\left(8^9-2^7\right)0=0\)
\(a.\)\(5^{2003}+5^{2002}+5^{2001}\)
\(=5^{2001}.\left(1+5+5^2\right)\)
\(=5^{2001}.31\)
\(\Rightarrow5^{2003}+5^{2002}+5^{2001}⋮31\)
\(b.\)
\(1+7+7^2+7^3+......+7^{101}\)
\(=8+7^2.\left(1+7\right)+7^4.\left(1+7\right)+....+7^{100}.\left(1+7\right)\)
\(=8+7^2.8+7^4.8+.....+7^{100}.8\)
\(=8+8.\left(7^2+7^4+...+7^{100}\right)\)
Ta thấy cả hai số hạng đều chia hết cho 8
\(\Rightarrow1+7+7^2+7^3+......+7^{101}⋮8\)
Mời bạn tham khảo các link sau:
a),b),c):https://hoidap247.com/cau-hoi/214111
d):https://olm.vn/hoi-dap/detail/78449788871.html
A = 412.412 B = 410.414
A = 410.412 + 412.2 B = 410.412 + 410.2
Vì 410.412 = 410.412 và 412.2 > 410.2 nên A > B