(3^-1)+(3^-2)+...+(3^-7)

Question

0

593

1

Guest Apr 12, 2015

+130516

+5

Best Answer

There is a "formula" for this given by

S_n = (a₁)(1 - r^n) / ( 1 - r) where Sn is the sum of the first n terms, a₁ is the first term, and r is the common ratio (1/3, in our case)

So we have

S₇ = (1/3) [(1 -(1/3)^7 ] / [ 1 - (1/3) ] = (1/3) [ 1 - 1/2187 ] / (2 /3) = [1 - 1/2187] / 2 = 1093/2187 = about .49977 ≈ .5

CPhill Apr 12, 2015

CPhill · Answer 1 · 2015-04-12T06:40:29

There is a "formula" for this given by

S_n = (a₁)(1 - r^n) / ( 1 - r) where Sn is the sum of the first n terms, a₁ is the first term, and r is the common ratio (1/3, in our case)

So we have

S₇ = (1/3) [(1 -(1/3)^7 ] / [ 1 - (1/3) ] = (1/3) [ 1 - 1/2187 ] / (2 /3) = [1 - 1/2187] / 2 = 1093/2187 = about .49977 ≈ .5