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

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

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

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

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

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

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

=> \(4B=-1-\dfrac{1}{3^{51}}\)

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

A. Số lượng số hạng là:

\(\left(51-1\right):2+1=26\) (số hạng)

Tổng: \(\left(51+1\right)\times26:2=676\)

B. \(1-2+3-4+5-...+51\) 

\(=1+\left(-2+3\right)+\left(-4+5\right)+...+\left(-50+51\right)\)

\(=1+1+1+...+1\) 

Số lượng số hạng (không tính số 1 đầu tiên) là: 

\(\left(51-2\right):1+1=50\) (số hạng)

Số lượng cặp là: \(50:2=25\) (cặp) 

Tổng là: \(1+25\times1=26\)

good

E=-1/3+1/3^2-1/3^3+1/3^4-...+1/3^50-1/3^51

3E=-1+1^2-1^3+1^4-1^5+...+1^50-1^51

3E=-1+1-1+1-1+...+1-1

3E=0

mình thiếu

bổ sung:

E=0:3

E=0

-----A=-1/3+1/3^2-1/3^3+-----+1/3^50-1/... 
A*1/3 =-1/3^2+1/3^3+--------------------+1/3^5...  
--------A=-1/3+1/3^2-1/3^3+...+1/3^50-1... 
-------A*1/3 =-1/3^2+1/3^3+..---------...+1/3^51-1/3^... 
---------------------------------------... 
A+A*1/3=-1/3+0...+0+...0---------------... 
A+A*1/3= -1/3-1/3^52 
4/3*A= -1/3-1/3^52 
Vậy 
A= -(1/3+1/3^52)*3/4.