SOLUTION: Hello! I’m really stumped on this. The question says to consider the infinite geometric series: sigma infinity n=1 -4(1/3)^n-1 and it says the lower limit of the summation

Question 1141362: Hello! I’m really stumped on this. The question says to consider the infinite geometric series:
sigma infinity n=1 -4(1/3)^n-1
and it says the lower limit of the summation notation is “n=1”. It then says to write the first four terms of the series, asks if the series diverge or converge, and if the series has a sum, find it. I think the series converge, and if I solved for the sum correctly, I got -5.9..., but I can’t figure out the first four terms right. Can you help? And have I solved the rest correctly?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Assuming this is right:

then your answer for the sum of the first four terms is correct (more precisely, the answer is -160/27 which is about -5.925925...).

The sum of n terms can be found from this:

where r is the common ratio (1/3) and is the first term (-4) ( so you do need to plug in n=1 to find )
Example:

You could also plug in n=1,2,3,4 into the summation and write it all out long-hand but its a lot of extra work.

As n-->, the term goes to zero, leaving just as the sum of the infinite progression:

RELATED QUESTIONS
Please help me work out this algebra problem in series. There is an infinity symbol on... (answered by ikleyn)

Algebra 2 question! Help me please! I have a test on this stuff later today and I am very (answered by Fombitz)

Consider the infinite geometric series Infinity E. -4(1/3) ^ n-1 n-1. Hopefully it... (answered by ewatrrr)

Consider the infinite geometric series Infinity (answered by Fombitz)

For questions 1 and 2 evaluate each infinte geometric series. 1. infinity (sign) sigma... (answered by robertb)

write the first six terms of the sequence 2. an=(n+1)^3 4. an=n/n+3 write the next (answered by richard1234)

Consider the infinite geometric series n=1 up to infinitey then the equation is... (answered by jim_thompson5910)

Find the sum of the infinite geometric series: 4/3−1/3+1/12−1/48... (answered by Edwin McCravy)

What is the sum of this infinite geometric series... (answered by ikleyn)