Question

tính tổng sau

a=2+2² + 2³+...+2¹⁰⁰

Answer 1

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

\(=>2.A=2.2+2^2.2+2^3.2+...+2^{100}.2\)

\(=>2.A=2^2+2^3+2^4+...+2^{101}\)

\(=>2.A-A=A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)

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

Vậy A=2¹⁰¹-2

Answer 2

2a=2^2+2^3+...+2^101

=>a=2^101-2

Answer 3

2a=2²+2³+...+2¹⁰¹=>a=2¹⁰¹-2

Answer 4

2a=2^2+2^3+...+2^101

=>a=2^101-2