Question

đề bài:  A = 1+2+2^2+...+2^299+2^300

Answer 1

A = 1+2+2²+...+2³⁰⁰

2A = 2+2²+2³+...+2³⁰¹

2A - A = 2³⁰¹-1

=> A = 2³⁰¹-1

Answer 2

\(A=1+2+2^2+...+2^{300}\)

\(\Leftrightarrow2A=\left(1.2\right)+\left(2.2\right)+\left(2^2.2\right)+...+\left(2^{300}.2\right)\)

\(\Leftrightarrow2A=2+2^2+....+2^{301}\)

\(\Leftrightarrow2A-A=\left(2+2^2+...+2^{301}\right)\)

\(2A-A=\left(2-2\right)+\left(2^2-2^2\right)+...+\left(2^{300}-2^{300}\right)+2^{301}-1\)

\(A=0+0+0+...+2^{301}-1\)

\(A=2^{301}-1\)

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