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\(B=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}+\dfrac{1}{6561}\)
\(3B=3\cdot\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{6561}\right)\)
\(3B=1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}+\dfrac{1}{2187}\)
\(3B-B=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{6561}\right)\)
\(2B=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(\dfrac{1}{9}-\dfrac{1}{9}\right)+...+\left(1-\dfrac{1}{6561}\right)\)
\(2B=0+0+...+1-\dfrac{1}{6561}\)
\(2B=1-\dfrac{1}{6561}\)
\(B=\left(1-\dfrac{1}{6561}\right):2\)
\(B=\dfrac{6560}{6561}:2\)
\(B=\dfrac{3280}{6561}\)
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C = 1 + 2 + 4 + 8 + ... + 1024
2 x C = 2 + 4 + 8 + ... + 1024 + 2048
2 x C - C = C = (2 + 4 + 8 + ... + 1024 + 2048) - (1 + 2 + 4 + 8 + ... + 1024) = 2048 - 1 = 2047
D = 1 + 3 + 9 + 27 + ... + 2187
3 x D = 3 + 9 + 27 + ... + 2187 + 6561
3 x D - D = 2 x D = (3 + 9 + 27 + ... + 2187 + 6561) - (1 + 3 + 9 + 27 + ... + 2187) = 6561 - 1 = 6560
D = 6560 : 2 = 3280
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Tham khảo tại đây
Giải toán trên mạng - Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath
Chúc học tốt!
Đặt \(B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)
\(\Rightarrow3B=3.\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)
\(\Rightarrow3B=3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\)
\(\Rightarrow3B-B=\left(3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\right)-\)\(\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)
\(\Rightarrow2B=3-\frac{1}{2187}\)
\(\Rightarrow B=\left(3-\frac{1}{2187}\right):2\)
\(\Rightarrow B=\frac{6560}{2187}\)
Chắc sai !!!
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Đặt \(V=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\)
\(\Rightarrow3V=3.\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\right)\)
\(\Rightarrow3V=1+\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}\right)\)
\(\Rightarrow3V=1+V-\dfrac{1}{2187}\)
\(\Rightarrow2V=1-\dfrac{1}{2187}\)
\(\Rightarrow V=\dfrac{1093}{2187}\).
A = 1/3 + 1/9 + 1/27 + 1/81 +...+1/729 + 1/2187
3A = 1 + 1/3 + 1/9 + 1/27 + 1/81 +...+1/729
=>2A = 1 - 1/2187
=> A = ....
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lấy MS chung là 2187, ta có:
729 + 243 + 81 + 9 + 3 + 1
________________________ = 1066/2187
2187
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P = 78 × 31 + 78 × 24 + 78 × 17 + 22 × 72
P = 78 × (31 + 24 + 17) + 22 × 72
P = 78 × 72 + 22 × 72
P = 72 × (78 + 22)
P = 72 × 100
P = 7200
S = 1 + 1/3 + 1/9 + 1/27 + ... + 1/2187
3S = 3 + 1 + 1/3 + 1/9 + ... + 1/729
3S - S = (3 + 1 + 1/3 + 1/9 + ... + 1/729) - (1 + 1/3 + 1/9 + 1/27 + ... + 1/2187)
2S = 3 - 1/2187
2S = 6560/2187
S = 6560/2187 : 2
S = 6560/2187 × 1/2
S = 3280/2187
S x 3 = 3 + 1 + 1/3 + 1/9 + 1/27 + ..................... + 1/729
S x 3 – S = 3 – 1/2187 = 6560/2187
Vậy S = 6560/2187 : 2 = 6560/4374