- #1
juantheron
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Calculate Natural no. $n$ for which $\displaystyle [\frac{n}{1!}]+[\frac{n}{2!}]+[\frac{n}{3!}]+...+[\frac{n}{10!}] = 2012$
where $[x] = $ Greatest Integer function
where $[x] = $ Greatest Integer function
The greatest integer function, also known as the floor function, is a mathematical function that rounds any given decimal number down to the nearest integer. It is represented by the symbol ⌊x⌋.
While the greatest integer function rounds down to the nearest integer, the ceiling function rounds up to the nearest integer. This means that the ceiling function would round 2.3 up to 3, while the greatest integer function would round it down to 2.
The greatest integer function is commonly used in computer programming and engineering to round down numbers to the nearest integer. It is also used in statistics and data analysis to group data into discrete categories.
Yes, the greatest integer function can be applied to negative numbers as well. For example, the greatest integer function of -3.5 would be -4, as it rounds down to the nearest integer.
The domain of the greatest integer function is all real numbers, while the range is the set of all integers. This means that any real number can be input into the function, but the output will always be an integer.