\(4-\dfrac{1}{4}-\dfrac{1}{28}-\dfrac{1}{70}-.....-\dfrac{1}{2002.2005}\)
\(=4-\left(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+.....+\dfrac{1}{2002.2005}\right)\)
\(=4-\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.....+\dfrac{1}{2002}-\dfrac{1}{2005}\right)\)\(=4-\left(1-\dfrac{1}{2005}\right)\)
\(=4-1+\dfrac{1}{2005}=3+\dfrac{1}{2005}=\dfrac{6016}{2005}\)
1/4+1/28+1/70+.....+1/550
D= 1/4+1/28+1/70+...+1/10300
Tính : 1/26+1/27+1/28+.......+1/50=1-1/2+1/3-1/4+.....+1/491/26+1/27+1/28+.......+1/50=1-1/2+1/3-1/4+.....+1/49
Tính
1, 14/7 + 5/9 + 4/9 - 2
2, 31/25 + ( 15/16 - 6/15 ) + 2/3
3, 23/28 - ( 23/28 - 1/3 ) + 2/3
4, 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
Cho a=1/11+1/12=1/13+1/14+..+1/70
Cmr 4/3<A<2,5
Cho biểu thức:
B=\(\dfrac{28^{28}+28^{24}+28^{20}+...+28^4+1}{28^{30}+28^{28}+28^{26}+...+28^2+1}\)
Tính giá trị biểu thức B
chứng tỏ
1/26 + 1/27 + 1/28 + ... + 1/50 =1 - 1/2 + 1/3 - 1/4 + .... + 1/49 - 1/50
Tính:
a, \(\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{99}+1\right)\)
b, \(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{100}-1\right)\)
c, \(C=\dfrac{4}{30}+\dfrac{4}{70}+\dfrac{4}{126}+...+\dfrac{4}{798}\)
\(b,\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+...+\left(x+\frac{1}{1024}\right)=1\)
\(a,\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(c,\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+...+\frac{1}{x.x+3}=\frac{34}{103}\)
\(d,\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
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