like is raised to a positive integer power , the expression expands as

where the coefficients are precisely the numbers in row of Pascal's triangle:

The entire left diagonal of Pascal's triangle corresponds to the coefficient of in these binomial expansions, while the next left diagonal corresponds to the coefficient of , and so on.

To see how the binomial theorem relates to the simple construction of Pascal's triangle, consider the problem of calculating the coefficients of the expansion of in terms of the corresponding

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