Tính bằng cách hợp lí:
14,58.460+7,29.540.2
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14,58.460+7,29.540.2
= 14,58 . 460 + 7,29 . 2 . 540
= 14,58 . 460 + 14,58 . 540
= 14,58 . ( 460 + 540 )
= 14,58 . 1000
= 14 580
# HOK TỐT #
\(12,25+\left(-21,37\right)-\left(14,67-21,75\right)\)
\(=12,25-21,37-14,67+21,75\)
\(=12,25+21,75-21,37-14,63-0,04\)
\(=34-36-0,04\)
= -2-0,04=-2,04
120:{54-[50:2.(3^2-2.4)]}
= 120:{ 54-[25.(9-8)]}
= 120:{54-[25.1]}
= 120:{54-25}
= 120:29
=\(\dfrac{120}{29}\)
e: \(=\dfrac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{10}\cdot3^8}=\dfrac{2^9\cdot3^8\left(2\cdot3-1\right)}{2^{10}\cdot3^8}=\dfrac{5}{2}\)
g: \(=125+\dfrac{3}{5}-97-\dfrac{2}{3}+97+\dfrac{2}{5}-125-\dfrac{1}{3}=0\)
\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{323}\\ =\dfrac{1}{2}\times\left(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+...+\dfrac{2}{17\times19}\right)\\=\dfrac{1}{2}\times\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{17}-\dfrac{1}{19}\right)\\ =\dfrac{1}{2}\times\left(\dfrac{1}{1}-\dfrac{1}{19}\right)\\ =\dfrac{1}{2}\times\dfrac{18}{19}=\dfrac{9}{19}\)
đề bài đây:
\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{323}\)
= (8x125)x(50x2)x(45x10+45)
= 1000x100x495
= 49.500.000