Question

H=1/3+1/9+1/27+....+1/2187

Answer 1

`H=1/3+1/9+1/27+....+1/2187`

`3H = 1 + 1/3 + 1/9 + ... + 1/729`

`3H - H = (1 + 1/3 + 1/9 + ... + 1/729) - (1/3+1/9+1/27+....+1/2187)`

`2H = 1 - 1/2187`

`2H = 2186/2187`

`H = 1093/2187`

Answer 2

\(H=\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^7}\)

\(3H=1+\dfrac{1}{3}+...+\dfrac{1}{3^6}\)

\(3H-H=1-\dfrac{1}{3^7}\)

\(2H=1-\dfrac{1}{3^7}\)

\(2H=\dfrac{3^7-1}{3^7}\)

\(H=\dfrac{3^7-1}{2.3^7}\)

Answer 3

truongdz153912/06/2022

H = 1/3 + 1/9 + 1/27 + ..... + 1/2187`

`3H = 3 xx ( 1/3 + 1/9 + 1/27 + .... + 1/2187 )`

`3H = 1 + ( 1/3 +1/9 + 1/27 + .... + 1/729 )`

`3H = 1 + A - 1/2187`

`2H = 1 - 1/2187`

`2H = 2186/2187`

H= 2186/2167 : 2`

`H= 1093/2167`

Vậy `H = 1093/2167`