Question

Tính tổng sau :

A = 2 + 2² + 2³ + ....... + 2¹⁰⁰

Các bạn giúp mình nha , mình cần ngay bây giờ !

Answer 1

A = 2¹ + 2² + 2³ + ..... + 2¹⁰⁰

2A = 2² + 2³ +2⁴ + ... + 2¹⁰⁰ + 2¹⁰¹

2A - A = A = ( 2¹⁰¹ + 2¹⁰⁰ + ... + 2² ) - ( 2¹⁰⁰ + 2⁹⁹  + ... + 2¹ )

A = 2¹⁰¹ - 2¹

A = 2¹⁰¹ - 2

Hok tốt!

Answer 2

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

\(\Rightarrow2A=2^2+2^3+..+2^{101}\)

\(\Rightarrow2A-A=2^{101}-1\)

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

Answer 3

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

\(\Rightarrow2A=2^2+2^3+2^4+.....+2^{100}+2^{101}\)

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

\(\Rightarrow A=2^{101}-2=2\times\left(2^{100}-1\right)\)

Answer 4

\(A=2+2^2+2^3+....+2^{99}+2^{100}\)

\(\Rightarrow2A=2^2+2^3+2^4+...+2^{100}+2^{101}\)

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

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