for the geometric series shown, state whether the series in convergent. If the Series is convergent give its sum
9+6.3 +4.41 +...
a tutor helped me earlier but how is the sum 0.7
9+6.3 +4.41 +...
= 9(1 + .7 + .49 + ..
= 9(1 + .7 + .7^2 + ...)
the bracket is a geometric series with a first term of 1 and a common ration of .7
S∞ = a/(1-r)
= 1/(1-.7)
= 1/.3
= 10/3
so the total sum is 9(10/3) = 30
The sum is is not 0.7. That is the ratio of successive terms.
I thought I answered the question earlier. The sum converges to 30
so wats 2+2
To determine if the geometric series is convergent, we need to check if the common ratio (r) is between -1 and 1.
For the given series 9 + 6.3 + 4.41 + ..., we can see that each term is obtained by multiplying the previous term by 0.7 (which is less than 1). Hence, the common ratio (r) is 0.7.
Now, to find the sum of a convergent geometric series, we can use the formula:
Sum = a / (1 - r)
where "a" is the first term of the series and "r" is the common ratio.
In this case, the first term (a) is 9 and the common ratio (r) is 0.7, so we can substitute these values into the formula:
Sum = 9 / (1 - 0.7)
Sum = 9 / 0.3
Sum = 30
Therefore, the sum of the given geometric series is 30.