Question

giúp em với ạ:tính

A=1/2+1/2^2+1/2^3+...+1/2^100

B=1+1/3+1/3^3+...+1/3^2022

 

Answer 1

A = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^100

2A = 1 + 1/2 + 1/2^2 + ... + 1/2^99
2A - A = (1 + 1/2 + 1/2^2 + ... + 1/2^99) - (1/2 + 1/2^2 + 1/2^3 + ... + 1/2^100)

A = 1 - 1/2^100

B = 1 + 1/3 + 1/3^3 + ... + 1/3^2022

3B = 3 + 1 + 1/3 + ... + 1/3^2021

3B - B = (3 + 1 + 1/3 + ... + 1/3^2021) - (1 + 1/3 + 1/3^3 + ... + 1/3^2022)

2B = 3 - 1/3^2022

B = \(\dfrac{\text{3 - 1/3^2022}}{\text{2}}\)

Answer 2

   A        =      \(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\) + \(\dfrac{1}{2^3}\) +...............+ \(\dfrac{1}{2^{100}}\)

2.A       = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\) +\(\dfrac{1}{2^3}\).........+\(\dfrac{1}{2^{99}}\)

2A -A   =  1 - \(\dfrac{1}{2^{100}}\)

       A  =   1 - \(\dfrac{1}{2^{100}}\)

B          =    1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^3}\) + ....+ \(\dfrac{1}{3^{2022}}\) 

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