Answer:
Explanation:
AI-generated answer
To find the value of the expression 5 (1 1 5 ) 5 (1 1 6 ) ⋯ … … … … . . 5 (1 1 624), let's break it down step by step.
First, let's focus on the expression 5 (1 1 5 ). This means multiplying 5 by 115.
5 (1 1 5 ) = 5 * 115 = 575
Next, we move on to the next part of the expression, 5 (1 1 6 ).
5 (1 1 6 ) = 5 * 116 = 580
Continuing this pattern, we can see that each term is 5 more than the previous term.
So, we can write the expression as:
5 (1 1 5 ) 5 (1 1 6 ) ⋯ … … … … . . 5 (1 1 624) = 575 * 580 * ...
Since each term is 5 more than the previous term, we can simplify this expression as:
(575 + 0) * (575 + 5) * (575 + 10) * ... * (575 + (624-1)*5)
Simplifying further, we have:
575 * 580 * 585 * ... * 3525
To find the value of this expression, we can divide each term by 5:
115 * 116 * 117 * ... * 705
Now, notice that we are multiplying consecutive numbers from 115 to 705. This is equivalent to calculating the product of all the numbers from 1 to 705 and then dividing it by the product of all the numbers from 1 to 114.
Using the formula for the product of consecutive numbers, we can write this as:
(705!)/(114!)
Now, let's simplify this expression:
(705 * 704 * 703 * ... * 1) / (114 * 113 * 112 * ... * 1)
Since we are dividing by the product of all the numbers from 1 to 114, all these terms cancel out:
(705 * 704 * 703 * ... * 115)
So, the value of the given expression is:
(705 * 704 * 703 * ... * 115)
And since we are multiplying consecutive numbers from 115 to 705, the value will be a large number.
Therefore, the answer is not (a) 2, (b) 3, or (c) 5. The answer is not provided in the question, so we cannot determine the exact value