2016+2016+...+2016+2016x99
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a, - { -(2016 +2015) - [ - (2016 - 2015) - (2016+2015) ] }
= -{-(2016+2015)-[-0-0]}
= -{-4031-0-0}
=-4031
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Ta có:A=\(\frac{2016^{2016}+2}{2016^{2016}-1}\)>1
=>A<\(\frac{2016^{2016}+2-2}{2016^{2016}-1-2}\)=\(\frac{2016^{2016}}{2016^{2016}-3}\)=B
=>A<B(công thức nếu \(\frac{a}{b}\)>1 thì \(\frac{a}{b}\)<\(\frac{a-n}{b-n}\)(nEN)
CM công thức:
Ta có \(\frac{a}{b}\)>1=>a>b=>a=b+n(nEN)
Ta so sánh \(\frac{a}{b}\) và \(\frac{a-n}{b-n}\)(nEN)
Mà a*(b-n)=ab-an=ab-(b+n)*n=ab-(bn+n2)=ab-bn-n2
b*(a-n)=ba-bn
Vì ab-bn-n2<ba-bn
=>\(\frac{a}{b}\)<\(\frac{a-n}{b-n}\)
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\(P=\dfrac{3^{2016}-6^{2016}+9^{2016}-12^{2016}+15^{2016}-18^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\dfrac{\left(3^{2016}-6^{2016}\right)+\left(9^{2016}-12^{2016}\right)+\left(15^{2016}-18^{2016}\right)}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\dfrac{3^{2016}\left(1-2^{2016}\right)+3^{2016}\left(3^{2016}-4^{2016}\right)+3^{2016}\left(5^{2016}-6^{2016}\right)}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\dfrac{3^{2016}\left(1-2^{2016}+3^{2016}-4^{2016}+5^{2016}-6^{2016}\right)}{-\left(1^{2016}-2^{2016}+3^{2016}-4^{2016}+5^{2016}-6^{2016}\right)}\)
\(=-3^{2016}\).
Vậy \(P=-3^{2016}\)
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\(2^{2016}+4^{2016}+6^{2016}+...+20^{2016}=2^{2016}\left(1+2^{2016}+3^{2016}+...+10^{2016}\right)\)
Do đó:
\(A=\frac{1^{2016}+2^{2016}+3^{2016}+...+10^{2016}}{2^{2016}+4^{2016}+6^{2016}+...+20^{2016}}=\frac{1}{2^{2016}}\)
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#)Giải :
3 x 2016 + 9 x 2016 + 20 x 2016 + 28 x 2016 + 38 x 2016 + 2016 + 2016
= ( 3 + 9 + 20 + 28 + 38 + 1 + 1 ) x 2016
= 100 x 2016
= 201600
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\(P=\frac{3^{2016}-6^{2016}+9^{2016}-12^{2016}+15^{2016}-18^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\frac{\left(1.3\right)^{2016}-\left(2.3\right)^{2016}+\left(3.3\right)^{2016}-\left(4.3\right)^{2016}+\left(5.3\right)^{2016}-\left(6.3\right)^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\frac{1^{2016}.3^{2016}-2^{2016}.3^{2016}+3^{2016}.3^{2016}-4^{2016}.3^{2016}+5^{2016}.3^{2016}-6^{2016}.3^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=\frac{-3^{2016}\left(-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}\right)}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)
\(=-3^{2016}\)
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2016 × 35 + 2016 × 65
= 2016 × (35+65)
= 2016 × 100
= 201600
2016 × 99 + 2016
= 2016 × 99 + 2016 × 1
= 2016 × (1+99)
= 2016 × 100
= 201600
2016 × 102 - 2016 × 2
= 2016 × (102-2)
= 2016 × 100
= 201600
2016 × 101 - 2016
= 2016 × 101 - 2016 × 1
= 2016 × (101-1)
= 2016 × 100
= 201600
2016 x 35 + 2016 x 65
= 2016 x ( 35 + 65 )
= 2016 x 100
= 201600
2016 x 99 + 2016
= 2016 x 99 + 2016 x 1
= 2016 x ( 99 + 1 )
= 2016 x 100
= 201600
2016 x 102 - 2016 x 2
= 2016 x ( 102 - 2 )
= 2016 x 100
= 201600
2016 x 101 - 2016
= 2016 x 101 - 2016 x 1
= 2016 x ( 101 - 1 )
= 2016 x 100
= 201600
Đề bài chưa cụ thể
bạn cho đề sai có bao nhiêu số 2016