A Pascal's triangle

Number Theory Level 2

What is the second last term of the 2017th row in a Pascal's triangle?


The answer is 2016.

V A by v a , 18, India

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3 solutions

Zico Quintina
May 2, 2018

The k + 1 k+1 st row in Pascal's Triangle consists of the binomial coefficients ( k 0 ) , ( k 1 ) , ( k 2 ) , … , ( k k − 1 ) , ( k k ) \binom{k}{0}, \binom{k}{1}, \binom{k}{2},\ldots, \binom{k}{k-1}, \binom{k}{k} ; so the second-to-last term in the 2017 2017 th row is ( 2016 2015 ) = 2016 \binom{2016}{2015} = 2016 .

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Giorgos K.
May 2, 2018

A bit outdated... why not asking for 2018th row?

or ask for 2019th row in order to get 2018 as an answer?

in this way your question has more chances to become popular...

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V A
May 1, 2018

For the 1st row, it is 0. For the 2nd row, it is 1. For the 3rd row, it is 2. For the 4th row, it is 3. So, for the n t h th row, it is n-1, and so for the 2017th row, it is 2017-1 = 2016 Ans : 2016

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