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\(F=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+......+\frac{3}{870}\)
\(=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+.....+\frac{3}{29.30}\)
\(=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{29}-\frac{1}{30}\right)\)
\(=3.\left(1-\frac{1}{30}\right)\)
\(=3.\frac{29}{30}\)
\(=\frac{29}{10}\)
Lời giải:
Gọi giá tiền 1 con gà và 1 con vịt lần lượt là $a$ và $b$ (đồng). Theo bài ra ta có:
$3\times a+8\times b = 870000$ (1)
$3\times a+6\times b=720000$ (2)
Lấy phép tính (1) trừ phép tính (2) ta được:
$2\times b=870000-720000$
$2\times b=150000$
$b=150000:2=75000$
$a=(720000-6\times 75000):3=90000$ (đồng)
870 - x : 11 x 87 = 261
x : 11 x 87 = 870 - 261
x : 11 x 87 = 609
x : 11 = 609 : 87
x : 11 = 7
x = 7 x 11
x = 77
x : 0.25 x 2.3 = 6.9
x : 0.25 = 6.9 : 2.3
x : 0.25 = 3
x = 3 x 0.25
x = 0.75
2 x (y + y) = 8.16
y + y = 8.16 : 2
y x 2 = 4.08
y = 4.08 : 2
y = 2.04
y x 1.5 + y + y x 7.5 = 59.8
y x (1.5 + 1 + 7.5) = 59.8
y x 10 = 59.8
y = 59.8 : 10
y = 5.98
m : 1/6 + m : 0.25 = 152
m : 1/6 + m : 1/4 = 152
m x 6 + m x 4 = 152
m x (6 + 4) = 152
m x 10 = 152
m = 152 : 10
m = 15.2
m : 1/3 + m : 0.25 = 1.4
m : 1/3 + m : 1/4 = 1.4
m x 3 + m x 4 = 1.4
m x (3 + 4) = 1.4
m x 7 = 1.4
m = 1.4 : 7
m = 0.2
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+...+ \(\dfrac{1}{812}\) + \(\dfrac{1}{870}\)
A = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\)+...+ \(\dfrac{1}{28\times29}\)+ \(\dfrac{1}{29\times30}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) +...+\(\dfrac{1}{28}\)-\(\dfrac{1}{29}\)+ \(\dfrac{1}{29}\) - \(\dfrac{1}{30}\)
A = 1 - \(\dfrac{1}{30}\)
A = \(\dfrac{29}{30}\)
A = \(\frac{6x\left(1+8+27\right)}{6x\left(12+96+324\right)}\)= \(\frac{36}{432}\)=\(\frac{1}{12}\)
\(=3x\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{870}\right)\)
=\(3x\left(\frac{1}{1x2}+\frac{1}{2x3}+....+\frac{1}{29x30}\right)\)
=\(3x\left(1-\frac{1}{2}-\frac{1}{3}-....-\frac{1}{30}\right)\)
\(=3x\left(1-\frac{1}{30}\right)=3x\frac{29}{30}=\frac{29}{10}\)