Ta có:
1/4 = 1/3( 1-1/4)
1/28 = 1/3( 1/4 - 1/7)
1/70 = 1/3( 1/7 - 1/10)
..............................
1/10300 = 1/3( 1/100 - 1/103)
Cộng vế với vế ta có:
S = 1/4+1/28+1/70+1/130+...+1/10300 = 1/3( 1-1/103)
S = 34/103
1/4+1/28+1/70+.....+1/550
4-<1/4>-<1/28>-<1/70>-...-<1/2002x2005>
1,Tính
A, 14/7 + 5/9 + 4/9 - 2
B, 31/25 + ( 15/16 - 6/15 ) + 1/16
C, 23/28 - ( 23/28 - 1/3 ) +2/3
D, 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
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
\(b,\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+...+\left(x+\frac{1}{1024}\right)=1\)
\(a,\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(c,\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+...+\frac{1}{x.x+3}=\frac{34}{103}\)
\(d,\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
HỘ MÌNH VỚI . GẤP . MAI MÌNH ĐI HỌC RỒI . THANKS TRƯỚC NÀ . MÌNH SẼ TICK CHO BẠN NÀO TRẢ LỜI ĐÚNG NHẤT VÀ NHANH NHẤT NHÉ 
1) \(B=\dfrac{1}{2^3}+\dfrac{1}{3^3}+\dfrac{1}{4^3}+\dfrac{1}{5^3}+...+\dfrac{1}{500^3}< \dfrac{1}{4}\)
2) \(D=\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+...+\dfrac{3^{98}+1}{3^{98}}< 100\)
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
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
