tổng các ps trên là ; \(\frac{364}{729}\)
đặt biểu thức đó là X
ta có :
\(3X=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(\Rightarrow3X-X=1-\frac{1}{729}\)
\(\Rightarrow X=\frac{728}{729}.\frac{1}{2}=\frac{364}{729}\)
tổng các ps trên là ; \(\frac{364}{729}\)
đặt biểu thức đó là X
ta có :
\(3X=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(\Rightarrow3X-X=1-\frac{1}{729}\)
\(\Rightarrow X=\frac{728}{729}.\frac{1}{2}=\frac{364}{729}\)
A = ( \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\) ) \(\frac{729}{364}+100:\subset5X\left(3-1\right)\)
Tính
a) \(\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+\frac{2}{81}+\frac{2}{243}+\frac{2}{729}\)
b) \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}\)
1.Tính nhanh
a)427-98
b)2*19*15+3*43*10+62*80
c)\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
d)\(\left(1-\frac{1}{9}\right)\cdot\left(1-\frac{2}{9}\right)\cdot\left(1-\frac{3}{90}\right)\cdot.........\cdot\left(1-\frac{2018}{9}\right)\)
Bài 1 : Tính nhanh các tổng sau :
a) S = \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+........+\frac{2}{2017x2019}\)
b A = \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+..........+\frac{1}{729}+\frac{1}{2187}\)
GẤP NA CÁC TÌNH YÊU !!! MOA MOA MOA !!!!!!! GẤP LẮM LUN Ớ !!!!
Chứng minh rằng:\(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+....+\frac{1}{1985}< \frac{9}{20}\)
mk làm thế này đúng ko mọi người
Đặt \(A=\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+......+\frac{1}{243}\)
\(A=\frac{1}{3}+\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)+\left(\frac{1}{11}+\frac{1}{13}+\frac{1}{15}+....+\frac{1}{27}\right)+\left(\frac{1}{29}+\frac{1}{31}+\frac{1}{33}+....+\frac{1}{81}\right)+\left(\frac{1}{83}+\frac{1}{85}+\frac{1}{87}+.....+\frac{1}{243}\right)\)
\(=>A>\frac{1}{3}+\frac{1}{9}.3+\frac{1}{27}.9+\frac{1}{81}.27+\frac{1}{243}.81=\frac{1}{3.5}=\frac{5}{3}\)
\(=>A>\frac{5}{3}>\frac{5}{4}=>A< \frac{5}{4}\)
\(=>\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+....+\frac{1}{397}< \frac{5}{4}\)
\(=>1+\frac{1}{3}+\frac{1}{7}+....+\frac{1}{397}< \frac{5}{4}\)
\(=>\frac{1}{5}.\left(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+....+\frac{1}{397}\right)< \frac{9}{4}.\frac{1}{5}\)
\(=>\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+......+\frac{1}{1985}< \frac{9}{20}\)
\(\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+\frac{2}{81}+\frac{2}{243}+\frac{2}{729}\)
\(\left[x+\frac{1}{3}\right]+\left[x+\frac{1}{15}\right]+\left[x+\frac{1}{35}\right]+...+\left[x+\frac{1}{575}\right]\)
\(=11xx+\left[\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right]\)
cách tính nhanh phân số \(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+...+\frac{1}{19683}\)
Tìm a
\(\left(a+\frac{1}{1.3}\right)+\left(a+\frac{1}{3.5}\right)+\left(a+\frac{1}{5.7}\right)+...+\left(a+\frac{1}{23.25}\right)=11.a+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right).\)