Tính C=5+5 mũ 2+5 mũ3+5 mũ 4+...+5 mũ 99+5 mũ 100
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a)64:2mũ5×30×4
= 64 : 32 x 30 x 4
= 240
b)3 mũ 2× 5 - 2 mũ 2×7+2 mũ 0 × 5
= 9 x 5 - 4 x 7 + 1 x 5
= 45 - 28 + 5
= 22
c)2 mũ 3-5 mũ 3÷5 mũ 2 + 12×2 mũ 2
= 8 - 125 : 25 + 12 x 4
= 8 - 5 + 48
= 51
d)2[(7-3 mũ 3÷3 mũ 2) chia 2 mũ 2 + 99]-100
= 2[( 7 - 27 : 9) : 4 + 99] - 100
= 2[4 : 4 + 99] - 100
= 2. 100 - 100
= 200 - 100
= 100
e)4[(3 + 3^7:3^4)chia 10 + 97]-300
= 4[( 3 + 3^3) : 10 + 97] - 300
= 4[ 30 : 10 + 97 ] - 300
= 4. 100 - 300
= 400 - 300
= 100
f)2^2 x 5 [(5 mũ 2 cộng 2 mũ 3) chia 11 - 2] - 3^2 x 2
= 4 x 5 [ (25 + 8 ) : 11 - 2] - 9 x 2
= 20 [ 33 : 11 - 2] - 18
= 20. 1 - 18
= 20 - 18
= 2
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gọi biểu thức trên là A , ta có :
\(A=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+\dfrac{5}{3^5}-...+\dfrac{99}{3^{99}}+\dfrac{100}{3^{100}}\\ 3A=1-\dfrac{2}{3}+\dfrac{3}{3^2}-\dfrac{4}{3^3}+...+\dfrac{99}{3^{98}}-\dfrac{100}{3^{99}}\\ \Rightarrow A+3A=\left(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\right)+\left(1-\dfrac{2}{3}+\dfrac{3}{3^2}-\dfrac{4}{3^3}+...+\dfrac{99}{3^{98}}-\dfrac{100}{3^{99}}\right)\\ \Rightarrow4A\cdot3=12A=3-1+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^{98}}-\dfrac{1}{3^{99}}\)
từ đó ta được :
\(16A=3-\dfrac{100}{3^{99}}-\dfrac{100}{3^{100}}\\ \Rightarrow A=\dfrac{\dfrac{3-101}{3^{99}}-\dfrac{100}{3^{100}}}{16}\\ \Rightarrow A=\dfrac{3}{16}-\dfrac{\dfrac{101}{3^{99}}-\dfrac{100}{3^{100}}}{16}< \dfrac{3}{16}\)
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a) \(\left(3^4.57-9^2.21\right):3^5\)
\(=\left(3^4.57-3^4.21\right):3^5\)
\(=\left[3^4\left(57-21\right)\right]:3^5\)
\(=3^4.36:3^5\)
\(=3^4.2^2.3^2:3^5\)
\(=3.4\)
\(=12\)
b) Ta có; \(1^3+2^3+...+9^3=2025\)
\(\Leftrightarrow2^3.\left(1^3+2^3+....+9^3\right)=2^3.2025\)
\(\Leftrightarrow2^3+4^5+...+18^3=16200\)
Ta có : C = 5 + 52 + 53 + 54 + ....... + 5100
=> 5C = 5. (5 + 52 + 53 + 54 + ....... + 5100)
=> 5C = 52 + 53 + 54 + ....... + 5101
=> 5C - C = 5101 - 5
=> 4C = 5101 - 5
=> C = \(\frac{5^{101}-5}{4}\)
\(C=5+5^2+5^3+5^4+...+5^{100}\)
\(5C=5^2+5^3+5^4+5^5+...+5^{101}\)
\(5C-C=\left(5^2+5^3+5^4+5^5+...+5^{101}\right)-\left(5+5^2+5^3+5^4+...+5^{100}\right)\)
\(4C=5^{101}-5\)
\(C\left(5^{101}-5\right):4\)