Question

tính \(P=2^2+2^3+2^4+....+2^{1975}\)

Answer 1

------S = 1 + 2 + 2^2 + 2^3 +......... 2^63
=> 2S = 2 x (1 + 2 + 2^2 + 2^3 + ........... + 2^63
=> 2S = 2 + 2^2 + 2^3 +............+ 2^63 + 2^64
------S = 1 + 2 + 2^2 + 2^3 +........+ 2^63
S = 2^64 - 1

Answer 2

P = 2² + 2³ + 2⁴ + ... + 2¹⁹⁷⁵

2P = 2 x ( 2² + 2³ + 2⁴ + ... + 2¹⁹⁷⁵ )

2P = 2³ + 2⁴ + 2⁵ + .... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶

2P - P = ( 2³ + 2⁴ + 2⁵ + ... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶ ) - ( 2² + 2³ + 2⁴ + 2⁵ + .... + 2¹⁹⁷⁵ )

P= 2¹⁹⁷⁶ - 2²

Answer 3

P = 2² + 2³ + 2⁴ + ... + 2¹⁹⁷⁵

2P = 2 x ( 2² + 2³ + 2⁴ + ... + 2¹⁹⁷⁵ )

2P = 2³ + 2⁴ + 2⁵ + .... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶

2P - P = ( 2³ + 2⁴ + 2⁵ + ... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶ ) - ( 2² + 2³ + 2⁴ + 2⁵ + .... + 2¹⁹⁷⁵ )

P= 2¹⁹⁷⁶ - 2²

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