Question

bài 8 . CHO

A=2+ 2 mũ 2+2 mũ 3+....+2 mũ 10

Answer 1

\(A=2+2^2+2^3+....+2^{10}\)

\(\Rightarrow2A=2^2+2^3+....+2^{11}\)

\(\Rightarrow A=2A-A=\left(2^2+2^3+....+2^{11}\right)-\left(2+2^2+2^3+....+2^{10}\right)\)

\(\Rightarrow A=2^{11}-2\)

Answer 2

A = 2 + 2² + 2³ + ... + 2¹⁰

=( 2 + 2² ) + ( 2³ + 2⁴ ) + ( 2⁵ + 2⁶ ) + ( 2⁷ + 2⁸ ) + ( 2⁹ + 2¹⁰ )

= 2 x ( 1 + 2 ) + 2³ x ( 1 + 2 ) + 2⁵ x ( 1 + 2 ) + 2⁷ x ( 1 + 2 ) + 2⁹ x ( 1 + 2 ) 

= 2 x 3 + 2³ x 3 + 2⁵ x 3 + 2⁷ x 3 + 2⁹ x 3

= 3 x ( 2 + 2³ + 2⁵ + 2⁷ + 2⁹ )

= 3 x ( 2 + 8 +32 + 128 + 512 )

= 3 x 682

= 2046