Question

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

Answer 1

A=2+2²+2³+...+2¹⁰⁰

2A=2²+2³+2⁴+...+2¹⁰¹

2A-A=(2²+2³+2⁴+...+2¹⁰¹)-(2+2²+2³+...+2¹⁰⁰)

A=2¹⁰¹-2

Answer 2

A=2+2²+2³....+2¹⁰⁰

2A=2²+2³+2⁴....+2¹⁰⁰+2¹⁰¹

2A-A=2¹⁰¹-2

A=2¹⁰¹-2

Answer 3

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Answer 4

A = 2 + 2² + 2³ +...+ 2¹⁰⁰

2A = 2² + 2³ + 2⁴ +...+ 2¹⁰¹

2A - A =  2² + 2³ + 2⁴ +...+ 2¹⁰¹ - 2 - 2² - 2³ -...- 2¹⁰⁰

A = 2¹⁰¹ - 2