Question

Find the sum of the 11terms of geometric sequence 1,1/2,1/4,1/8,1/16

Answer 1

S₁₁ =
`(2047)/(1024)`

Explanation:

the sum of n terms in a geometric sequence is

`S_(n)` =
`(a_(1)(1 - r^(n)) )/(1-r)`

a₁ is the first term , r the common ratio , n the term number

here a₁ = 1 and r =
`(a_(2) )/(a_(1) )` =
`((1)/(2) )/(1)` =
`(1)/(2)`

substitute these value into the formula for
`S_(n)`

S₁₁ =
`(1(1-((1)/(2)) ^(11)) )/(1-(1)/(2) )`

=
`(1(1-(1)/(2048)) )/((1)/(2) )`

=
`(2((2048)/(2048)-(1)/(2048)) )/(1)`

=
`\frac{2((2047)/(2048)) }{}`

=
`(2047)/(1024)`