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\(A=1+\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}+...+\dfrac{1}{625}+\dfrac{1}{78125}\)
\(=1+\dfrac{1}{5}+\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^7}\)
\(5A=5+1+\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^6}\)
\(\Leftrightarrow5A-A=5+1+\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^6}-1-\dfrac{1}{5}-\dfrac{1}{5^2}-\dfrac{1}{5^3}-...-\dfrac{1}{5^7}\)
\(\Leftrightarrow4A=5-\dfrac{1}{5^7}\Leftrightarrow A=\dfrac{5-\dfrac{1}{5^7}}{4}=\dfrac{\dfrac{390624}{78125}}{4}=\dfrac{390624}{312500}=\dfrac{97656}{78125}\)
\(a,50\%+\dfrac{7}{12}-\dfrac{1}{2}\\ =\dfrac{1}{2}+\dfrac{7}{12}-\dfrac{1}{2}\\ =\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\dfrac{7}{12}\\ =\dfrac{7}{12}\\ b,2022\times67+2022\times43-2022\times10\\ =2022\times\left(67+43-10\right)\\ =2022\times100\\ =202200.\\ c,125-25:3\times12\)
\(=25\times5-25:3\times12\\ =25\times\left(5-\dfrac{1}{3}\right)\times12\\ =25\times\dfrac{14}{3}\times12\\ =1400\)
a,50%+127−21=21+127−21=(21−21)+127=127b,2022×67+2022×43−2022×10=2022×(67+43−10)=2022×100=202200.c,125−25:3×12
(689 + 875) + 125 = 689 + (875 + 125) = 689 + 1000 = 1689.
581 + (878 + 419) = (581 + 419) = 878 = 1000 + 878 = 1878.
a) = 875 + 5 x 15 - 875
= ( 875 - 875 ) + 5 x 15
= 0 + 5 x 15
= 75
b) = 19,83 x ( 79 + 21 ) + ( 0,87542 + 0,12458 ) x 17
= 19,83 x 100 + 1,00000 x 17
= 1983 + 17
= 2000
A, 32 * 47 + 32 * 53
= 32 * ( 47 + 53 )
= 32 * 100
= 3200 .
B, 875 + 5375 : 25 - 875
= 875 - 875 + 5375 : 25
= 0 + 2115
= 215 .
C, 5 * 25 * 2 * 16 * 4
= ( 5 * 2 * 16 ) * ( 25 * 4 )
= 160 * 100
= 16000 .