Question by Cristiano Ronaldo - Discuss with MathYouLike

Cristiano Ronaldo

19/03/2017 at 10:52

Evaluate 1+2+2²+2³+2⁴+...+2²⁰⁰⁰.

rational numbers

List of answers

caubevodanh3 19/03/2017 at 11:31

Put : A= 1 +2 + 2²+ 2³+ ..... + 2²⁰⁰⁰

=> 2A = 2 x ( 1+ 2 + 2²+ 2³+....+ 2²⁰⁰⁰)

2A = 2 + 2² + 2³ + ..... + 2²⁰⁰¹

=> 2A-A= (2 + 2² + 2³ + ..... + 2²⁰⁰¹)- ( 1 +2 + 2² + 2³ + ..... + 2²⁰⁰⁰)

=> A = 2²⁰⁰¹- 1
FA KAKALOTS 03/02/2018 at 12:45

Put : A= 1 +2 + 22 + 23 + ..... + 22000

=> 2A = 2 x ( 1+ 2 + 22 + 23 +....+ 22000 )

2A = 2 + 22 + 23 + ..... + 22001

=> 2A-A= (2 + 22 + 23 + ..... + 22001)- ( 1 +2 + 22 + 23 + ..... + 22000)

=> A = 22001 - 1

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