The millers house is 25 yards from mrs shapiro’s Haus how many feet apart are the two houses
2 answers:
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Answer: The correct option is
(d) This is a divergent geometric series. The sum cannot be found.
Step-by-step explanation: The given infinite geometric series is
We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.
We have the D' Alembert's ratio test, states as follows:
Let, is an infinite series, with complex coefficients
and we consider the following limit:
Then, the series will be convergent if L < 1 and divergent if L > 1.
For the given series, we have
So, the limit is given by
Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.
Thuds, (d) is the correct option.
The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
Given,
In the question:
The quadratic sequence is :
3, 11, 25, 45, ...
To find the nth term of the quadratic sequence.
Now, According to the question;
The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.
The difference between the first and second terms can be calculated as follows:
11-3 = 8
The difference between the second and third terms can be calculated as follows:
25-11 = 14
The difference between the third and fourth terms can be calculated as follows:
45-25 = 20
The sequence is expressed as follows:
3,3+8,11+11,25+20,...
The difference between consecutive terms expands by 6.
Use the principle of mathematical induction.
6
= 3n(n+1)
The sequence's nth term can be calculated as follows:
term = 3n(n+1) - 4n + 1
= 3n² - n + 1
Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
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