B=-1/3+1/3^2-.....-1/3^51

3B=-1/3^2+1/3^3-.....-1/3^52

3B-B=(-1/3^2+1/3^3-....-1/3^52)-(-1/3+1/3^2-....-1/3^51)

2B= -1/3^52-1/3

2B= -1/3^52-3^51/3^52

2B= -1-3^51/3^52

B= -3^51-1/3^52x2

B = \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{50}}\)

3B = \(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{49}}\)

2B = 3B - B = \(1-\frac{1}{3^{50}}\)

=> B = \(\frac{1-\frac{1}{3^{50}}}{2}\)

Làm ra dễ mà

\(B=\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+...+\dfrac{1}{3^{50}}-\dfrac{1}{3^{51}}\)

\(=\dfrac{1}{\left(-3\right)}+\dfrac{1}{\left(-3\right)^2}+\dfrac{1}{\left(-3\right)^3}+...+\dfrac{1}{\left(-3\right)^{50}}+\dfrac{1}{\left(-3\right)^{51}}-\dfrac{1}{3}\)

\(=\dfrac{1}{\left(3\right)^2}+\dfrac{1}{\left(3\right)^3}+...+\dfrac{1}{\left(-3\right)^{51}}+\dfrac{1}{\left(-3\right)^{52}}\)

\(\Rightarrow\dfrac{4}{3}B=\dfrac{1}{-3}-\dfrac{1}{\left(-3\right)^{52}}=\dfrac{-3^{51}-1}{3^{52}}\Rightarrow B=\dfrac{-3^{51}-1}{4.3^{51}}\)

\(B=-\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+....+\dfrac{1}{3^{50}}-\dfrac{1}{3^{51}}\)

=> \(3B=-1+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^{49}}-\dfrac{1}{3^{50}}\)

=> \(4B=-1-\dfrac{1}{3^{51}}\)

=> \(B=\dfrac{-1-\dfrac{1}{3^{51}}}{4}\)

\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}\)

\(3.A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{49}}\)

\(2A=3A-A=1-\dfrac{1}{3^{49}}\)

\(\Rightarrow A=\dfrac{1-\dfrac{1}{3^{50}}}{2}\)

\(B=\dfrac{5}{3}+\dfrac{5}{3^2}+...+\dfrac{5}{3^{50}}=5\left(\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}\right)\)

Căn cứ vào câu A thì các trong ngặc bằng \(\dfrac{1-\dfrac{1}{3^{50}}}{2}\)

suy ra \(B=\dfrac{5\left(1-\dfrac{1}{3^{50}}\right)}{2}\)

tick mik nha

hoi kho day

A = 1 × 2 × 3 + 2 × 3 × 4 + .....+ 48 × 49 × 50

ta có 4 x A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x (5 -1) + .....+ 48 × 49 × 50 x (51 - 47)

= 1 x 2 x 3 x 4 +  2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + ... + 48 x 49 x 50 x 51 - 47 x 48 x 49 x 50

= 48 x 49 x 50 x 51

suy ra A = (48 x 49 x 50 x 51) : 4

              = 12 x 49 x 50 x 51

nhớ k cho mik nha rùi mik lm nốt cho

A = 1 × 2 × 3 + 2 × 3 × 4 + .....+ 48 × 49 × 50

ta có 4 x A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x (5 -1) + .....+ 48 × 49 × 50 x (51 - 47)

= 1 x 2 x 3 x 4 +  2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + ... + 48 x 49 x 50 x 51 - 47 x 48 x 49 x 50

= 48 x 49 x 50 x 51

suy ra A = (48 x 49 x 50 x 51) : 4

              = 12 x 49 x 50 x 51

A= 24640

các bạn cho minhf cách làm nhé!