Question

cho a= 1+3+3^2+3+3^3................................+3^2015

b=3^2016 :2

tinh b-a

 

Answer 1

Ta có : A = 1 + 3 + 3² + ....... + 3²⁰¹⁵

=> 3A =  3 + 3² + ....... + 3²⁰¹⁶

=> 3A - A = 3²⁰¹⁶ - 1

=> 2A = 3²⁰¹⁶ - 1

=> A = 3²⁰¹⁶ - 1/2

Mà B = 3²⁰¹⁶/2

=> B - A =  3²⁰¹⁶/2 - 3²⁰¹⁶ - 1/2

=> B - A = 1/2 

Answer 2

Ta có: 3a-a=3²⁰¹⁶-1 <=> a=\(\frac{3^{2016}-1}{2}\)

=> b-a=\(\frac{3^{2016}}{2}-\frac{3^{2016}-1}{2}=\frac{1}{2}\)

Answer 3

 a= 1+ 3 + 3 + 3^2 +.... + 3^2015

=> 3a = 3+ 3^2 + 3^3 +..... + 3^2016

=> 3a - a = (3+ 3^2 + 3^3 +.... + 3^2016) - ( 1 + 3+ 3^2 +......+ 3^ 2015)

=> 2a = 3^2016 - 1

=> a= \(\frac{3^{2016}-1}{2}\)< b= \(\frac{3^{2016}}{2}\)

vậy a< b

Answer 4

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