Question

[Nguyễn Đặng Bảo Trâm]

Câu 1: (2 điểm) Tính nhanh tổng sau:

Answer 1

[Nguyễn Thị Thương Hoài]

 A =       1 + \(\dfrac{1}{3}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{27}\)+\(\dfrac{1}{81}\)+\(\dfrac{1}{243}\)+\(\dfrac{1}{729}\)

3 x A = 3 + 1 + \(\dfrac{1}{3}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{27}\)+\(\dfrac{1}{81}\)+\(\dfrac{1}{243}\)

3xA - A = 3 - \(\dfrac{1}{729}\)

A x ( 3 - 1) = \(\dfrac{3\times729}{729}\)- \(\dfrac{1}{729}\)                       
A x 2 = \(\dfrac{2186}{729}\) 
A = \(\dfrac{2186}{729}\): 2            

A = \(\dfrac{2186}{729}\)x\(\dfrac{1}{2}\)         
A =        \(\dfrac{1093}{729}\)                                                

Answer 2

[Nguyễn Công Danh]

gọi số cần tìm là A :

A= 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

A = 3 x ( 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 )

A = 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

A = 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 - 1 - 1/9 -1/27 - 1/81 - 1/243 - 1/729

A = 3 - 1/729 

A = 142/729