Question

\(A=2+2^2+2^3+2^4+........+2^{2020}\) 

\(A=?\)
 

Answer 1

\(A=2+2^2+2^3+...+2^{2020}\)

\(2A=2^2+2^3+2^4+...+2^{2021}\)

\(2A-A=\left(2^2+2^3+2^4+...+2^{2021}\right)-\left(2+2^2+2^3+...+2^{2020}\right)\)

\(A=2^{2021}-2\)

Answer 2

A = 2 + 2² + 2³ + 2⁴ +. . . . . + 2²⁰²⁰

2A = 2 . ( 2 + 2² + 2⁴ + ....... + 2²⁰²⁰ )

2A = 2² + 2³ + 2⁴ + 2⁵ +...... + 2²⁰²¹

2A - A = ( 2² + 2³ + 2⁴ + 2⁵ +......+2²⁰²¹) - ( 2 + 2² + 2³ +..... + 2²⁰²⁰)

A = ( 2² - 2² ) + (2³ - 2³ ) +.......+ ( 2²⁰²⁰ - 2²⁰²⁰ ) + 2²⁰²¹ - 2

A = 0 + 0 + ...... + 0 + 2²⁰²¹ - 2

A = 2²⁰²¹ - 2

Answer 3

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