I need help!can someone help me?thank you
2 answers:
For the sake of showing work I will replace the empty space with an x like so...
To find out what x is you must cross multiply (aka butterfly)
1*x = 2*6
1x = 12
x = 12
***If you don't understand the "cross multiply" technique let me know in the comments and I'll be happy to explain.
To make these fractions equivalent the empty spot must be 12
Hope this helped!
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Answer:
The series CONVERGES with the sum being 6.25.
Step-by-step explanation:
Given that the geometric series is 10 - 6 + 3.6 - 2.16 + ....
So the first term of the geometric progression is, = 10
The second term of the geometric progression is = -6 =
× r = 10 × r
where r is the constant ratio.
Therefore r = = -0.6
The third term of the geometric progression, = 3.6 =
× r = -6 × -0.6 = 3.6
The fourth term of the geometric progression, = -2.16 =
× r = 3.6 × -0.6 = -2.16
So the above confirms that the series is indeed a geometric progression with first term, = 10 and constant ratio, r = -0.6
Now to find if the series converges or diverges we can take sum of the series from first term to infinity.
We can already infer that the series is convergent since the constant ratio, r = -0.6 which is less than 1.
So from the formula for the sum to infinity of a geometric progression, S, we get
S =
So the series is convergent with the sum being 6.25