Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
The sum of the given series is 49 and it converges to infinity.
According to the statement
we have given that a series which is 7, -8, 64/7, 512/49
And we have to find that the series is converges or diverges.
So, For this purpose,
The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:
So,
[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]
[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]
[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]
And so on then
Sum of the series become to the nth partial sum
[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]
Multiplying both sides by -8/7 gives
[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]
and subtracting this from [tex]S_{N}[/tex] gives
[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]
[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]
Now the sum of the series is 49 and the it converges to infinity.
So, The sum of the given series is 49 and it converges to infinity.
Learn more about the Convergence of series here
https://brainly.com/question/23804543
#SPJ1
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.