sum of 1 to n natural number is 28 then find the value of n
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Answer:
If the sum of 1 to n natural numbers is 36, then what is the value of n?
If the sum of 1 to n natural numbers is 36, then what is the value of n?
I’ll start by answering a more general question:
If 1+2+…+n=k, then 8k+1−−−−−√−12=n
In this case,
8×36+1−−−−−−−−√−12=289−−−√−12= 8
You may ask how I came up with this amazing way to undo the summing of the first n numbers.
I’m glad you asked!
Let the function T(n) be defined as giving the sum of the first n numbers. T(n) is often called the nth “triangular” number, because if you arrange objects in a triangle, like bowling p
Using S to represent the sum of the natural numbers from 1 to n, we have:
S = 1 + 2 + … + (n-1) + n [A]
We can express this in another way.
S = n + (n-1) + … + 2 + 1 [B]
Adding A + B:
2S = [1+n] + [2+(n-1)] + … + [(n-1)+2] + [n+1] = n(n+1)
As S = 36, 2S = 72
So, we need to solve the equation n(n+1) = 72.
There are two possible solutions to this equation:
n=8
n=-9
We can safely ignore the second answer as -9 is not a natural number.
Answer: n=8
Answer:
1+2+3+4+5+6+7=28
1-n=28
n=7
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