Easy maths question
eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc
I think it's sum of N-i from i=1 to N-1
How many when N=100?
Can I simplify this in terms of N only and what's the function called in maths and/or in Excel or google sheets?
Probably easy but it's been years since i did maths.
Thanks!
Just guessing it seems to be N choose 2, that googles to the right answer for 100
Is that right?
=SUMPRODUCT(LARGE(A1:A100,ROW(INDIRECT("2:100"))))
If N choose 2 is the right answer then i can just use that formula, i assume Excel has the function, else a factorial version
Why you need to send close request? right away accept Shaun's solution and it will close automatically.
Principal
In a network with N nodes, what's the maximum number of connections you can make?Consider this:
eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc
I think it's sum of N-i from i=1 to N-1
Starting with "n" nodes, each node added gets N nodes.
Each node added, adds "n" connections.
So the formula is a sum of added connections.
The number of connections is a sequence: 1,2,3,6,12,
1 to 2 adds 1 for 1 total
2 to 3 adds 2 for 3 total
3 to 4 adds 3 for 6 total
4 to 5 adds 4 for 10 total
99 to 100 adds 99 >> so we will call M=N-1 as the sequence ends at N-1
SUM over k=1:M (1:k-1) which is done with a well-known formula M*(M+1)/2
Check:
M=1>>1*(1+1)/2=1
M=2>>2*(2+1)/2=3
M=3>>3*(3+1)/2=6
M=4>>4*(4+1)/2=10
.
M=99>>99*(99+1)/2=4,950
In this case, you have to be careful because there are N nodes and N-1 added connections. Thus M=N-1
How many when N=100?4,950
Can I simplify this in terms of N onlyYes. As above.
what's the function called in mathsPartial sum of integers
and/or in Excel or google sheets? SUM
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