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MATH / For each integer n, let f(n) be the sum of the elements of the nth row (i.e. the row with n+1 elements) of Pascal's triangle minus the sum of all the elements from previous rows. F…

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problem

For each integer nn, let f(n)f(n) be the sum of the elements of the nnth row (i.e. the row with n+1n+1 elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example, \[f(2) = \underbrace{(1 + 2 + 1)}_{\text{2nd row}} - \underbrace{(1 + 1 + 1)}_{\text{0th and 1st rows}} = 1. \]What is the minimum value of f(n)f(n) for n≥2015n \ge 2015?
Plain-text mathematical notation (without MathML)
For each integer n, let f(n) be the sum of the elements of the nth row (i.e. the row with n+1 elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example, \[f(2) = \underbrace{(1 + 2 + 1)}_{\text{2nd row}} - \underbrace{(1 + 1 + 1)}_{\text{0th and 1st rows}} = 1. \]What is the minimum value of f(n) for n≥2015?
Original LaTeX notation
For each integer $n$, let $f(n)$ be the sum of the elements of the $n$th row (i.e. the row with $n+1$ elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example, \[f(2) = \underbrace{(1 + 2 + 1)}_{\text{2nd row}} - \underbrace{(1 + 1 + 1)}_{\text{0th and 1st rows}} = 1. \]What is the minimum value of $f(n)$ for $n \ge 2015$?

level

Level 4

type

Counting & Probability

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Source and history

task_id
1a4a023b-ed4f-5e07-9ce1-d2bfdea39183
task_key
counting~5fand~5fprobability--test--1a4a023b-ed4f-5e07-9ce1-d2bfdea39183
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import