Question

1)tính tổng biết S = 1+2+2^2+....+2^9+2^10

Answer 1

S = 1 + 2 + 2² + ... + 2⁹ + 2¹⁰

2S = 2 . ( 1 + 2 + 2² + ... + 2⁹ + 2¹⁰ )

2S = 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹

2S - S = ( 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹ ) - ( 1 + 2 + 2² + ... + 2⁹ + 2^{10 )}

S = 2¹¹ - 1

Answer 2

S = 1 + 2 + 2² + ... + 2⁹ + 2¹⁰

2S = 2 . ( 1 + 2 + 2² + ... + 2⁹ + 2¹⁰ )

2S = 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹

2S - S = ( 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹ ) - ( 1 + 2 + 2² + ... + 2⁹ + 2^{10 )}

S = 2¹¹ - 1

Answer 3

S = 1 + 2 + 2² + ... + 2⁹ + 2¹⁰

2S = 2 . ( 1 + 2 + 2² + ... + 2⁹ + 2¹⁰ )

2S = 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹

2S - S = ( 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹ ) - ( 1 + 2 + 2² + ... + 2⁹ + 2^{10 )}

S = 2¹¹ - 1

Answer 4

S = 1 + 2 + 2² + ... + 2⁹ + 2¹⁰

2S = 2 . ( 1 + 2 + 2² + ... + 2⁹ + 2¹⁰ )

2S = 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹

2S - S = ( 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹ ) - ( 1 + 2 + 2² + ... + 2⁹ + 2^{10 )}

S = 2¹¹ - 1

Answer 5

S = 1 + 2 + 2² + ... + 2⁹ + 2¹⁰

2S = 2 . ( 1 + 2 + 2² + ... + 2⁹ + 2¹⁰ )

2S = 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹

2S - S = ( 2 + 2² + 2³ + ... + 2¹⁰ + 2¹¹ ) - ( 1 + 2 + 2² + ... + 2⁹ + 2^{10 )}

S = 2¹¹ - 1

Answer 6

Ta có: S = 1 + 2 + 2² + ........ + 2¹⁰

=> 2S = 2 + 2² + 2³ +........ + 2¹¹

=> 2S - S = 2¹¹ - 1

=> S = 2¹¹ - 1

Answer 7

Ta có: S = 1 + 2 + 2² + ........ + 2¹⁰

=> 2S = 2 + 2² + 2³ +........ + 2¹¹

=> 2S - S = 2¹¹ - 1

=> S = 2¹¹ - 1

Answer 8

S = 1 + 2 + 2 ^ 2 + ... + 2 ^ 9 + 2 ^ 10

2S = 2 + 2 ^ 2 + 2 ^3 +... + 2 ^ 10 + 2 ^ 11

2S - S = ( 2 + 2 ^ 2 + 2 ^3 +... + 2 ^ 10 + 2 ^ 11 )

           -  ( 1 + 2 + 2 ^ 2 + ... + 2 ^ 9 + 2 ^ 10 )

S         = 2 ^ 11 - 1

s          = 2047

Answer 9

2S=2.(1+2+2²+...+2⁹+2¹⁰)

2S=2+2²+2³+...+2¹⁰+2¹¹

S=2S-S

S=(2+2²+2³+...+2¹⁰+2¹¹) - (1+2+2²+...+2⁹+2¹⁰)

S=2+2²+2³+...+2¹⁰+2¹¹-1-2-2²-...-2⁹-2¹⁰

S=-1+2¹¹

S=-1+2048

S=2047