In a network with N nodes, what's the maximum number of connections you can make?

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!

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!

```
=SUMPRODUCT(LARGE(A1:A100,ROW(INDIRECT("2:100"))))
```

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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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