Question

[minamoto shizuka]

Tính tổng:

S = 1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + .......... + 2¹⁰⁰

Answer 1

[TAKASA]

S = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + ... + 2^100 

2S = 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... + 2^100 + 2^101 

2S - S = ( 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... + 2^100 + 2^101 ) - ( 1 + 2 + 2^2 +2^3 +2^4 + 2^5 + .... + 2^100 ) 

S = 2^101 - 1 

Vậy S = 2^101 - 1

Answer 2

[Huỳnh Quang Sang]

Ta có :

S = 1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰⁰

2S = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰¹

2S - S =  ( 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰¹ ) -  ( 1 - 2 - 2² - 2³ - 2⁴ - 2⁵ - ... - 2¹⁰⁰ )

S = 2^{101 -} 1