Question

find the sum of the infinite geometric series

Answer 1

find r

Answer 2

okay....

Answer 3

i got 3 3/4

Answer 4

i got that too

Answer 5

We notice, once again that the common ratio is:\[\bf Common \ ratio=r= \frac{ \frac{ -5 }{ 3 } }{ 5 }=-\frac{ 1 }{ 3 }\]So the terms of the geometric series will be given by ('a' is the first term; 'r' is the common ratio):\[\bf ar^{n-1}=5\left( -\frac{ 1 }{ 3 } \right)^{n-1}\]Since the geometric series is convergent, i.e. \(\bf |r|<1\), the limit of the partial sums of the series can be evaluated as:\[\bf S_n=\frac{a}{1-r}\]Can you evaluate the sum?

@mathisfun13

Answer 6

It's the same procedure for most geometric series questions. You should be able to do them by yourself now.

Answer 7

okay

Answer 8

sum_{i=0}^{\infty}(-1)^i \frac{5}{3^i}

Answer 9

\[\sum_{i=0}^{\infty}(-1)^i \frac{5}{3^i}\]

Answer 10

3 3/4 is correct though :)

Answer 11

Yup, which means he has learnt the way to do it. Good job son.