Question

S= 1 + 2 + 2² + 2³ + 2⁴ +...+ 2²⁰¹⁶

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Answer 1

S = 1 + 2 + 2² + 2³ + 2⁴ + ... + 2²⁰¹⁶

2S = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰¹⁷

2S - S = (2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰¹⁷) - (1 + 2 + 2² + 2³ + 2⁴ + ... + 2²⁰¹⁶)

S = 2²⁰¹⁷ - 1

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Answer 2

S= 1 + 2 + 2² + 2³ + 2⁴ +...+ 2²⁰¹⁶

2S=( 1 + 2 + 2² + 2³ + 2⁴ +...+ 2²⁰¹⁶)

2S=2+2²+...+2²⁰¹⁷

2S-S=(2+2²+...+2²⁰¹⁷)-(1 + 2 + 2² + 2³ + 2⁴ +...+ 2²⁰¹⁶)

S=2²⁰¹⁷-1

Answer 3

S=1 + 2 + 2² +2³ +...+ 2²⁰¹⁶

2S=2 + 2² + 2³ + 2⁴ +...+2²⁰¹⁷

2S - S = 2²⁰¹⁷ -1