=13/24

13/24

Mình cảm ơn mình biết trước rồi

Ha Ha Ha

= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}\)\(\frac{1}{18}\)

= \(\frac{1}{3}-\frac{1}{18}\)

= \(\frac{5}{18}\)

kết quả là 439/2808

[{1/4-1/4}+ { 1/6-1/6}+{1/9-1/9}+{1/13-1/13}]*11/4=0

ta có\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}\)

\(=\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)

tách

\(B=\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)

\(2B=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\)

\(2B-B=\frac{1}{2}-\frac{1}{1024}\)

thay vào B ta có 

\(\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{1024}=\frac{1}{1024}\)

\(A=\frac{1}{2}-\frac{1}{4}-\cdot\cdot\cdot-\frac{1}{1024}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{2^2}-\cdot\cdot\cdot-\frac{1}{2^{10}}\)

\(\Rightarrow2A=1-\frac{1}{2}-\cdot\cdot\cdot-\frac{1}{2^9}\)

\(\Rightarrow2A-A=\left(1-\frac{1}{2}-\cdot\cdot\cdot-\frac{1}{2^9}\right)-\left(\frac{1}{2}-\frac{1}{2^2}-\cdot\cdot\cdot-\frac{1}{2^{10}}\right)\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2^{10}}\)

\(\Rightarrow A=\frac{1}{2}+\frac{1}{2^{10}}\)

\(\Rightarrow A=\frac{2^9+1}{2^{10}}\)

\(\Rightarrow A=\frac{513}{1024}\)

Đặt: \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\)

\(\Rightarrow A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\)

\(\Rightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\right)\)

\(=1+\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{10}}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{10}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{11}}\right)\)

\(\Rightarrow A=1-\frac{1}{2^{11}}=\frac{2^{11}-1}{2^{11}}=\frac{2047}{2048}\)
 

\(2A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)

\(2A-A=\left(1+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+...+\frac{1}{2048}\right)\)

\(A=1-\frac{1}{2048}=\frac{2047}{2048}\)

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{2048}\)

\(=\left(1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{2048}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

Phân số thứ 20 à , hơi khó đó

Nhưng kết quả là:\(\frac{1}{1599}\) 

Kết quả đúng là \(\frac{1}{1599}\)

mình làm rùi 

ủng hộ nha

toan lop 6 day a co ma lop 5 y ngu hay sao ma hoi

S = 1\(\dfrac{1}{3}\).1\(\dfrac{1}{8}\).1\(\dfrac{1}{15}\).1\(\dfrac{1}{24}\).1\(\dfrac{1}{35}\)....

S = \(\dfrac{4}{3}\).\(\dfrac{9}{8}\).\(\dfrac{16}{15}\).\(\dfrac{25}{24}\).\(\dfrac{36}{35}\)....

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)...

Phân số thứ 100 của dãy số trên là: \(\dfrac{101^2}{100.102}\)

Tích của 100 số đầu tiên của dãy trên là:

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)....\(\dfrac{101^2}{100.102}\)

S = \(\dfrac{\left(1.2.3...100.101\right)\times\left(2.3.4.5...101\right)}{\left(1.2.3.4...100\right)\times\left(3.4.5....101.102\right)}\)

S = \(\dfrac{101.2}{1.102}\)

S = \(\dfrac{101}{51}\)

51xS = \(\dfrac{101}{51}\) x 51 = 101

S = 1\(\dfrac{1}{3}\).1\(\dfrac{1}{8}\).1\(\dfrac{1}{15}\).1\(\dfrac{1}{24}\).1\(\dfrac{1}{35}\)....

S = \(\dfrac{4}{3}\).\(\dfrac{9}{8}\).\(\dfrac{16}{15}\).\(\dfrac{25}{24}\).\(\dfrac{36}{35}\)....

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)...

Phân số thứ 100 của dãy số trên là: \(\dfrac{101^2}{100.102}\)

Tích của 100 số đầu tiên của dãy trên là:

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)....\(\dfrac{101^2}{100.102}\)

S = \(\dfrac{\left(1.2.3...100.101\right)\times\left(2.3.4.5...101\right)}{\left(1.2.3.4...100\right)\times\left(3.4.5....101.102\right)}\)

S = \(\dfrac{101.2}{1.102}\)

S = \(\dfrac{101}{51}\)

51xS = \(\dfrac{101}{51}\) x 51 = 101

Kết quả bằng 4. Đúng 100%

S = 1\(\dfrac{1}{3}\).1\(\dfrac{1}{8}\).1\(\dfrac{1}{15}\).1\(\dfrac{1}{24}\).1\(\dfrac{1}{35}\)....

S = \(\dfrac{4}{3}\).\(\dfrac{9}{8}\).\(\dfrac{16}{15}\).\(\dfrac{25}{24}\).\(\dfrac{36}{35}\)....

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)...

Phân số thứ 100 của dãy số trên là: \(\dfrac{101^2}{100.102}\)

Tích của 100 số đầu tiên của dãy trên là:

S = \(\dfrac{2^2}{1.3}\).\(\dfrac{3^2}{2.4}\).\(\dfrac{4^2}{3.5}\).\(\dfrac{5^2}{4.6}\).\(\dfrac{6^2}{5.7}\)....\(\dfrac{101^2}{100.102}\)

S = \(\dfrac{\left(1.2.3...100.101\right)\times\left(2.3.4.5...101\right)}{\left(1.2.3.4...100\right)\times\left(3.4.5....101.102\right)}\)

S = \(\dfrac{101.2}{1.102}\)

S = \(\dfrac{101}{51}\)

51xS = \(\dfrac{101}{51}\) x 51 = 101