Answer:
292,968
Step-by-step explanation:
As we know,
Sum of a geometric sequence (S) =
where,
a = first term of sequence,
r = the constant ratio,
n = number of terms in sequence.
So, according to the question,
a = 3,
r = 5,
n = 8.
by substituting the values in the above formula, we get;
⇒
⇒
The committee can be selected by combinatorial argument in
ways.
A counting-based argument is known as a combinatorial argument or combinatorial proof. This line of reasoning has previously been used, for instance in the section on Stirling numbers of the second sort.
By initially selecting k individuals from our group of n, we can then choose one of those k individuals to serve as the committee's chairperson.
A number of methods for completing the first task, k methods for completing the second task, and so on. ways to create a k-member committee with a chairperson.
is the number of methods to construct a committee with a chairman of size less than or equal to n can be found by adding up over 1≤k≤n.
A committee of size less than or equal to n can also be formed with a chairperson by selecting the chairperson first, followed by the members of the committee. The chairperson can be chosen from among n options. The picker has two options for the remaining n-1 individuals: to include them or not. We therefore have n options for the chairperson, 2 options for the following, 2 options for the following, etc. These can be multiplied together to give us , which is a proof of the identity.
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