Description: Compute the binomial coefficient " ( N + 1 ) choose 2 " from " N choose 2 ": N + ( N 2 ) = ( (N+1) 2 ). (Contributed by Alexander van der Vekens, 8-Jan-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | bcn2p1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0cn | |
|
2 | 2z | |
|
3 | bccl | |
|
4 | 2 3 | mpan2 | |
5 | 4 | nn0cnd | |
6 | 1 5 | addcomd | |
7 | bcn1 | |
|
8 | 1e2m1 | |
|
9 | 8 | a1i | |
10 | 9 | oveq2d | |
11 | 7 10 | eqtr3d | |
12 | 11 | oveq2d | |
13 | bcpasc | |
|
14 | 2 13 | mpan2 | |
15 | 6 12 14 | 3eqtrd | |