Answers: 1
![\rm :\longmapsto\:\displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]](/tpl/images/2490/1626/ad95d.png)
![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{1 - \dfrac{1}{3} } \bigg]](/tpl/images/2490/1626/5f958.png)
![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{\dfrac{3 - 1}{3} } \bigg]](/tpl/images/2490/1626/dbb5e.png)
![\rm :\longmapsto\:S_n = \dfrac{1}{3} \bigg[\dfrac{1 - {\bigg[\dfrac{1}{3} \bigg]}^{n} }{\dfrac{2}{3} } \bigg]](/tpl/images/2490/1626/d56be.png)
![\bf\implies \:S_n = \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](/tpl/images/2490/1626/bfed7.png)
![\bf :\longmapsto\:\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } = \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](/tpl/images/2490/1626/3ecfb.png)
![\purple{\rm :\longmapsto\:\displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]}](/tpl/images/2490/1626/504ee.png)
![\rm \: = \: \displaystyle\lim_{n \to \infty }\rm \dfrac{1}{2}\bigg[1 - \dfrac{1}{ {3}^{n} } \bigg]](/tpl/images/2490/1626/243db.png)
![\rm \: = \: \rm \dfrac{1}{2}\bigg[1 - 0 \bigg]](/tpl/images/2490/1626/58975.png)
![\purple{\rm :\longmapsto\:\boxed{\tt{ \displaystyle\lim_{n \to \infty }\rm \bigg[\dfrac{1}{3} + \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } + - - + \dfrac{1}{ {3}^{n} } \bigg]} = \frac{1}{2}}}](/tpl/images/2490/1626/93945.png)
Another question on Mathematics
Mathematics, 20.06.2019 18:04
An astronaut drops a rock into a crater on the moon. the distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t)0.82. what is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?
Answers: 1
Mathematics, 21.06.2019 14:30
The last time i bought this product , it cost $20.00 but it looks like it cost 29. 60 today? what is the increase
Answers: 2
Mathematics, 21.06.2019 23:40
The function f(x) is shown in this graph the function g(x)=6x
Answers: 2
Mathematics, 22.06.2019 00:00
In a timed typing test lara typed 63 words per minute.estimate the number of words she should be able to type in half in hour show your work
Answers: 2
You know the right answer?
Lim n-> infinity [1/3 + 1/3² + 1/3³ + . . . .+ 1/3ⁿ]...
Questions
Mathematics, 06.01.2021 23:40
English, 06.01.2021 23:40
English, 06.01.2021 23:40
Mathematics, 06.01.2021 23:40
Chemistry, 06.01.2021 23:40
Computers and Technology, 06.01.2021 23:40
English, 06.01.2021 23:40
Mathematics, 06.01.2021 23:40
Mathematics, 06.01.2021 23:40
Mathematics, 06.01.2021 23:40
English, 06.01.2021 23:40
Computers and Technology, 06.01.2021 23:40
Social Studies, 06.01.2021 23:40
Mathematics, 06.01.2021 23:40
