Question

Tính:

A = 2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ + ......+ 2² - 2¹

Giúp mk vs các bn ơi huhu!!!!

Answer 1

Ta có:

A =2¹⁰⁰-2⁹⁹+2⁹⁸-2⁹⁷+.....+2²-2¹

=>2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+.....+2³-2²

=>2A+A=(2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+.....+2³-2²) + (2¹⁰⁰-2⁹⁹+2⁹⁸-2⁹⁷+....+2²-2¹⁾

^=>3A=2¹⁰¹-2

=>A=\(\frac{2^{101}-2}{3}\)

Vậy A=\(\frac{2^{101}-2}{3}\).

 

Answer 2

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(\Rightarrow2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(\Rightarrow2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)\)

\(\Rightarrow3A=2^{101}-2\)

\(\Rightarrow A=\frac{2^{101}-2}{3}\)

Answer 3

tick nha

Answer 4

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2^1\)

\(\Rightarrow2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(\Rightarrow2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-1\right)\)

\(\Rightarrow3A=2^{101}-1\)

\(\Rightarrow A=\frac{2^{101}-1}{3}\)