319 × 3
.................
.................
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\(\Leftrightarrow9A=3^3+3^5+...+3^{21}\\ \Leftrightarrow9A-A=3^3+3^5+...+3^{21}-3-3^3-3^5-...-3^{19}\\ \Leftrightarrow8A=3^{21}-3\Leftrightarrow A=\dfrac{3^{21}-3}{8}\)
a, 4130 + 4130 + 4130 + 319 + 319 + 319
= 4130 × 3 + 319 × 3
= (4130 + 319) × 3
= 4449 × 3
= 13347
b, 1052 + 1052 – ( 286 + 286 + 286)
= 1052 × 2 – 286 × 3 = 2104 – 858
= 1246
c, 2020 + 2020 + 2010 + 2010 + 56 + 56
= 2020 × 2 + 2010 × 2 + 56 × 2
= (2020 + 2010 + 56) × 2
= 4086 × 2
= 8172
d, 2830 + 2830 + 2830 + 2830 +2830 = 2830 × 5 = 14150a
3A = 3+32+33+34+...+320+321
3A - A = (3+32+33+34+...+320+321) - ( 1+3+32+33+...+319+220)
2A = 321-1
A = \(\dfrac{31^{21}-1}{2}\)
\(3\times\left(\frac{1}{5\times8}+\frac{1}{8\times11}+....+\frac{1}{97\times100}+x\right)=\frac{319}{100}\)
\(\Rightarrow\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+...+\frac{3}{97\times100}\right)+3\times x=\frac{319}{100}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{97}-\frac{1}{100}+3\times x=\frac{319}{100}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{100}+3\times x=\frac{319}{100}\)
\(\Rightarrow\frac{19}{100}+3\times x=\frac{319}{100}\)
\(\Rightarrow3\times x=\frac{319}{100}-\frac{19}{100}\)
\(\Rightarrow3\times x=3\)
\(\Rightarrow x=3:3\)
\(\Rightarrow x=1\)
Vậy x = 1
Đáp án: 957