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11^2+22^2=11^2+22^2
22^2+33^2=22^2+33^2
......
88^2+99^2=88^2+99^2
\(\dfrac{25^3.2^{10}}{16^2.625^2}=\dfrac{25^3.2^{10}}{2^8.25^2}=\dfrac{25.2^2}{1}=25.4=100.\)
(26 + 53 ) +(42 -26-55-53)
=79 + ( 16 -55 - 53 )
=79 + (-39-53)
=79 -39 - 53
=40 - 53 = -13
\(D=\left(4\cdot25\right)\cdot\left(8\cdot125\right)\cdot\left(5\cdot42\right)\cdot2\)
\(D=100\cdot1000\cdot210\cdot2\)
\(D=100\cdot1000\cdot420\)
\(D=100000\cdot420\)
\(D=42000000\)
D=2.4.5.8.25.42.125
D=(2.5)(4.25)(8.125).42
D=10.100.1000.42
D=42000000
2/35 + 4/77 + 2/143 + 4/221 + 2/323 + 4/437 + 2/575
= 2/5.7 + 4/7.11 + 2/11.13 + 4/13.17 + 2/17.19 + 4/19.23 + 2/23.25
= 1/5 - 1/7 + 1/7 - 1/11 + 1/11 - 1/13 + 1/13 - 1/17 + 1/17 - 1/19 + 1/19 - 1/23 + 1/23 - 1/15
= 1/5 - 1/25
= 4/25
\(\frac{2}{35}\)+ \(\frac{4}{77}\)+ \(\frac{2}{143}\)+ \(\frac{4}{221}\)+ \(\frac{2}{323}\)+ \(\frac{4}{437}\)+ \(\frac{2}{575}\).
= \(\frac{2}{5.7}\)+ \(\frac{4}{7.11}\)+ \(\frac{2}{11.13}\)+ \(\frac{4}{13.17}\)+ \(\frac{4}{17.21}\)+ \(\frac{2}{21.23}\).
= \(\frac{1}{5}\)- \(\frac{1}{7}\)+ \(\frac{1}{7}\)- \(\frac{1}{11}\)+ \(\frac{1}{11}\)- \(\frac{1}{13}\)+ \(\frac{1}{13}\)- \(\frac{1}{17}\)+ \(\frac{1}{17}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{23}\).
= \(\frac{1}{5}\)- \(\frac{1}{23}\).
= \(\frac{23}{115}\)- \(\frac{5}{115}\).
= \(\frac{18}{115}\).
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