Lời giải:
Gọi tổng trên là $A$
$5A=\frac{5}{5.10}+\frac{5}{10.15}+\frac{5}{15.20}+....+\frac{5}{2010.2015}$
$5A=\frac{10-5}{5.10}+\frac{15-10}{10.15}+...+\frac{2015-2010}{2010.2015}$
$5A=\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2010}-\frac{1}{2015}$
$5A=\frac{1}{5}-\frac{1}{2015}=\frac{402}{2015}$
$A=\frac{402}{10075}$
\(\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+\frac{1}{15\cdot20}+...........+\frac{1}{2005\cdot2010}\)
\(\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+\frac{1}{15\cdot20}+......+\frac{1}{2005\cdot2010}\) cho mình xin công thức nhak.
Bài 1
a) Tìm x, biết
\(\frac{2\cdot x-4,36}{0,125}\)= 0,25 * 42,9 - 11,7 * 0,25 + 0,25 * 0,8
b) Tính nhanh
\(N=\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+\frac{1}{15\cdot20}+...+\frac{1}{2005\cdot2010}\)
Bài 2
a) Tìm x, biết (x + 5,2) : 3,2 = 4,7 (dư 0,5).
b) Tính nhanh:\(A=\frac{4047991-2010\cdot2009}{4050000-2011\cdot2009}\)
Bài 3
a) Tìm x, biết 104,5 x X - 14,1 × X + 9,6 x X = 25
b) Tính nhanh
\(T=\frac{2009\cdot2010+2000}{2011\cdot2010-2020}\)
\(\dfrac{\left(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}\right):\left(\dfrac{1}{6}+\dfrac{1}{10}-\dfrac{1}{15}\right)}{\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}\right):\left(\dfrac{1}{4}-\dfrac{1}{6}\right)}=\)
\(\dfrac{15}{14}\) : \(\dfrac{10}{21}\) x \(\dfrac{1}{5}\)
\(5\) x \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\)
\(7\) : \(\dfrac{1}{5}\) - \(\dfrac{1}{5}\)
\(6\) + \(\dfrac{1}{5}\) : \(2\)
\(8\) - \(\dfrac{1}{5}\) x \(7\)
\(\dfrac{y}{2022}-\dfrac{1}{10}-\dfrac{1}{15}-\dfrac{1}{21}-...-\dfrac{1}{120}=\dfrac{5}{8}\)
\(\dfrac{2}{5}\)*\(15\dfrac{1}{3}\)-\(\dfrac{2}{5}\)*\(10\dfrac{1}{3}\)
\(12\dfrac{5}{11}\)-(\(3\dfrac{1}{4}\)+\(2\dfrac{5}{11}\)]
\(\dfrac{34}{31}\)-\(\dfrac{19}{28}\)-\(\dfrac{3}{31}\)
Tính nhanh
a, S= \(\dfrac{1}{3}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{35}\) + \(\dfrac{1}{63}\) + \(\dfrac{1}{99}\) + \(\dfrac{1}{143}\)
b, A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{21}\) + \(\dfrac{1}{28}\)
c, H =\(\dfrac{4047991-2010x2009}{4050000-2011x2009}\)
d, T = \(\dfrac{2009x20010+2000}{2011x2010-2020}\)
e, P = \(\dfrac{7589-80,5x69,3}{7485,05-79x69,3}\)
f, B = 5,1 x 42,2 + 1,7 x 448 x 3 - 0,15 x 700
Giúp mình với
Tính:
(2007 - 2005) + (2003 - 2001) +...+ (7 - 5) + (3 - 1)
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Viết tiếp 3 số hạng thứ 8;9 và 10 của dãy số sau: \(\dfrac{1}{1x5};\dfrac{1}{5x9};\dfrac{1}{9x13};...\)
Tính hợp lí :
A = \(\dfrac{-2}{9}\) + \(\dfrac{-3}{4}\) + \(\dfrac{3}{5}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{57}\) + \(\dfrac{1}{3}\) + \(\dfrac{-1}{36}\)
B = \(\dfrac{1}{2}\) + \(\dfrac{-1}{5}\) + \(\dfrac{-5}{7}\) + \(\dfrac{1}{6}\) + \(\dfrac{-3}{35}\) + \(\dfrac{1}{3}\) + \(\dfrac{1}{41}\)
C = \(\dfrac{-1}{2}\) + \(\dfrac{3}{5}\) + \(\dfrac{-1}{9}\) + \(\dfrac{1}{127}\) + \(\dfrac{-7}{18}\) + \(\dfrac{4}{35}\) + \(\dfrac{2}{7}\)
