Question

Tính tổng: A = 1 + 2 + 2² + 2³ + 2⁴ + .......+ 2⁹⁹

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Answer 1

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

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

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

=> 2A - A = ( \(2+2^2+2^3+...+2^{100}\)) - ( \(1+2+2^2+...+2^{99}\))

=> A = \(2+2^2+2^3+...+2^{100}-1+2+2^2+...+2^{99}\)

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

Answer 2

A= 1+2+2²+2³+2⁴+...+2⁹⁹

2A=2+2²+2³+2⁴+2⁵+...+2¹⁰⁰

2A-A=(2+2²+2³+2⁴+2⁵+...+2¹⁰⁰)-(1+2+2²+2³+2⁴+...+2⁹⁹)

2A-A=2+2²+2³+2⁴+2⁵+...+2¹⁰⁰-1-2-2²-2³-2⁴-...-2⁹⁹

A=2¹⁰⁰-1