Considering the special case of Pascal’s triangle (k = 5)

and adding side-by-side the resulting equations for j = 5, 6,…, 10, check that the following identity holds true:

Using a similar method, generalize the previous result to show that for any positive integers n and k with k ≤ n, we have

Apply this result to reestablish the well-known identities

Transcribed Image Text:

5 (3)-('3') = ('7'). j5, 4