tính tổng
C= 1/3+1/9+1/27+1/81+1/243
tính tổng dãy số sau:
C=1/3+1/9+1/27+1/81+1/243
bạn quy đồng mẫu số tất cả cả các phân số trên lên thành 243 rồi cộng vào là được
\(C=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(C=\frac{81}{243}+\frac{27}{243}+\frac{9}{243}+\frac{3}{243}+\frac{1}{243}\)
\(C=\frac{81+27+9+3+1}{243}=\frac{121}{243}\)
Vậy C = ...
Bài giải
\(C=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(C=\frac{1}{3}+\frac{1}{3\cdot3}+\frac{1}{3\cdot3\cdot3}+\frac{1}{3\cdot3\cdot3\cdot3}+\frac{1}{3\cdot3\cdot3\cdot3\cdot3}\)
\(3C=1+\frac{1}{3}+\frac{1}{3\cdot3}+\frac{1}{3\cdot3\cdot3} +\frac{1}{3\cdot3\cdot3\cdot3}\)
\(3C-C=1-\frac{1}{243}\)
\(2C=\frac{242}{243}\)
\(C=\frac{242}{243}\text{ : }2=\frac{121}{243}\)
bài 1 : tính nhanh tổng:
1+1/3+1/9+1/27+1/81+1/243+1/729
1 + 1/3 + 1/9+1/27+1/81+1/243+1/729
=1+1-1/3+1/3-1/9+1/9-1/27-1/27-1/81+1/81-1/243
= 2 - 1/243
=485/243
Tính tổng bằng cách hợp lí:
S= 1/3+1/9+1/27+1/81+........+1/243
S = 1/3+1/9+1/27+1/81+1/243+1/729+1/2187 ( 1 )
Nhân S với 3. Ta có:
S x 3 = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 ( 2 )
Trừ ( 2 ) với ( 1 ) ta có:
S x 3 - S = 1 - 1/ 2187
2S = 2186/ 2187
S = 2186/ 2187 : 2
S = 1093/ 2187
tính nhanh C = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
Đặt A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
A x 3 = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729
= 1 - 1/729
A x 2 = 728/729
A = 364/729
Câu 3. (2 điểm) Tính nhanh tổng sau
S = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) +\(\dfrac{1}{81}\) + \(\dfrac{1}{243}\)+ \(\dfrac{1}{729}\)
S= 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
S= 3 x ( 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 )
S = 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
S= 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 - 1 - 1/9 -1/27 - 1/81 - 1/243 - 1/729
S = 3 - 1/729
S= 142/729
tính nhanh tổng sau
1 + 1 phần 3 + 1 phần 9 + 1 phần 27 +1 phần 81 + 1 phần 243 + 1 phần 729
\(=1\frac{364}{729}\)\(=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}=1+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}=1\frac{ }{ }\)
1/3+1/9+1/27+1/81+1/243+1/729.Tính nhanh
tham khảo
Đặt A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
A x 3 = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729
= 1 - 1/729
A x 2 = 728/729
A = 364/729
\(\dfrac{243}{729}+\dfrac{81}{729}+\dfrac{27}{729}+\dfrac{9}{729}+\dfrac{2}{729}+\dfrac{1}{729}=\dfrac{243+81+27+9+2+1}{729}=\dfrac{363}{729}=\dfrac{121}{243}\)
Tính hơp lý : A = 1/3+1/9+1/27+1/81+1/243
\(A=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\\ =\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+\dfrac{1}{3^5}\\ =>3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\\ =>3A-A=2A=1-\dfrac{1}{3^5}\\ =>A=\dfrac{1-\dfrac{1}{3^5}}{2}=\dfrac{3^5-1}{2.3^5}\)
tính nhanh
a= 1/3+1/9+1/27+1/81+1/243+1/729
=.........?
\(3A=3\cdot\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729}\right)\)
\(\Rightarrow3A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)
Lấy \(3A-A=1-\dfrac{1}{729}\)
\(\Rightarrow2A=\dfrac{728}{729}\Rightarrow A=\dfrac{364}{729}\)
A=1/3+1/9+1/27+1/81+1/243+1/729
3A=1+1/3+1/9+1/27+1/81+1/243
3A-A=(1+1/3+1/9+1/27+1/81+1/243)-(1/3+1/9+1/27+1/81+1/243+1/729)
3A-A=1-1/3+1/3-1/9+1/9-1/27+1/27-1/81+1/81-1/243+1/243-1/729)
2A=1-1/729
2A=728/729
A=728/729/2
A=364/729