Question

Cho S=1+2+2^2+2^3+.....2^100  so sánh S với 2^101

 

Answer 1

2S=2+2^2+2^3+...+2^101

2S-S=2^101-1

S=2^101-2<2^101

hok tốt

Answer 2

\(S=1+2+2^2+\cdot\cdot\cdot+2^{100}\)

\(\Rightarrow2S=2+2^2+2^3+\cdot\cdot\cdot+2^{101}\)

\(\Rightarrow2S-S=\left(2+\cdot\cdot+2^{101}\right)-\left(1+\cdot\cdot\cdot+2^{100}\right)\)

\(\Rightarrow S=2^{101}-1\)<\(2^{101}\)

\(\Rightarrow S\)<\(2^{101}\)

Answer 3

S = 1 + 2 + 2² + .... + 2¹⁰⁰

=> 2S = 2 + 2² + 2³ + ... + 2¹⁰¹

Lấy 2S trừ S theo vế ta có : 

2S - S = (2 + 2² + 2³ + ... + 2¹⁰¹) - (2 + 2² + 2³ + ... + 2¹⁰¹)

        S = 2¹⁰¹ - 1

=> S < 2¹⁰¹

Answer 4

S = 1 + 2 + 2² + 2³ + ... + 2¹⁰⁰ 

2S = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰¹

2S - S = ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰¹ ) - ( 1 + 2 + 2² + 2³ + ... + 2¹⁰⁰ )

S = 2¹⁰¹ - 1

=> S < 2¹⁰¹

Vậy ....

Answer 5

\(S=1+2+2^2+2^3+...+2^{100}\)

\(2S=2+2^2+2^3+2^4+...+2^{101}\)

\(2S-S=\left(2+2^2+2^3+2^4+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)\)

\(S=2^{101}-1\)

Vì \(2^{101}-1< 2^{101}\)

\(\Rightarrow S< 2^{101}\)

Vậy \(S< 2^{101}\)

Answer 6

       S=1+2+2²+2³+....+2¹⁰⁰

     2S=    2+2²+2³+....+2¹⁰⁰+2¹⁰¹

 2S-S=2¹⁰¹-1

      S=2¹⁰¹-1 < 2¹⁰¹

=> S<2¹⁰¹