There is a formula connecting any (k+1) successive coefficients in the nth row of Pascal's Triangle with a coefficient in the (n+k)th row. find this formula.

My name is Timothy . This is a secondary level question (11th grade) A Student is asking this.

Hi Tim,

You should repeatedly apply Pascal's Identity on two coefficients in the nth row adding up to one in the next row to see what happens to k+1 successive coefficients. Now apply the same technique to the k coefficients you have just produced the the (n+1)st row. Continue to repeat with successive rows. Once you've got to the (n+k)th row, work backwards to see how many each of the coefficients in the nth row you need to get the one you ended up with on the (n+k)th row.


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