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\(VT=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{101}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{102}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{101}+\frac{1}{102}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{102}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}+\frac{1}{102}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{51}\)
\(=\frac{1}{52}+\frac{1}{53}+\frac{1}{54}+...+\frac{1}{102}\)
\(=VP\)
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\(\frac{17}{21}\cdot\frac{48}{53}+\frac{17}{21}\cdot\frac{4}{53}+\frac{52}{53}\cdot\frac{4}{21}\)
\(=\frac{17}{21}\left(\frac{48}{53}+\frac{4}{53}\right)+\frac{52}{53}\cdot\frac{4}{21}\)
\(=\frac{17}{21}\cdot\frac{52}{53}+\frac{52}{53}\cdot\frac{4}{21}\)
\(=\frac{52}{53}\left(\frac{17}{21}+\frac{4}{21}\right)\)
\(=\frac{52}{53}\cdot1\)
\(\frac{17}{21}.\frac{48}{53}+\frac{17}{21}.\frac{4}{53}+\frac{52}{53}.\frac{4}{21}\)
= \(\frac{17}{21}.\left(\frac{48}{53}+\frac{4}{53}\right)+\frac{52}{53}.\frac{4}{21}\)
= \(\frac{17}{21}.\frac{52}{53}+\frac{52}{53}.\frac{4}{21}\)
=\(\frac{52}{53}.\left(\frac{17}{21}+\frac{4}{21}\right)\)
= \(\frac{52}{53}\)
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\(3A=3+3^2+3^3+...+3^{21}\\ 2A=3^{21}-1\\ A=\dfrac{3^{21}-1}{2}\\ 5B=5^2+5^3+...+5^{11}\\ 4B=5^{11}-5\\ B=\dfrac{5^{11}-5}{4}\\ 2C=2^5+2^6+...+2^{31}\\ C=2^{31}-2^4\)
53 : 5 + 52 . 102 - 25 . 3
= 10,6 + 5,304 - 75
= 15,904 - 75
= - 59 , 096
= -59 , 096