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MATH / Let A = lceil log_2 2 rceil + lceil log_2 3 rceil + dots + lceil log_2 1000 rceiland B=⌊log₂2⌋+⌊log₂3⌋+…+⌊log₂1000⌋.Compute A−B.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let \[A = \lceil \log_2 2 \rceil + \lceil \log_2 3 \rceil + \dots + \lceil \log_2 1000 \rceil\]and B=⌊log22⌋+⌊log23⌋+…+⌊log21000⌋.B = \lfloor \log_2 2 \rfloor + \lfloor \log_2 3 \rfloor + \dots + \lfloor \log_2 1000 \rfloor.Compute A−B.A-B.
Plain-text mathematical notation (without MathML)
Let \[A = \lceil \log_2 2 \rceil + \lceil \log_2 3 \rceil + \dots + \lceil \log_2 1000 \rceil\]and B=⌊log₂2⌋+⌊log₂3⌋+…+⌊log₂1000⌋.Compute A−B.
Original LaTeX notation
Let \[A = \lceil \log_2 2 \rceil + \lceil \log_2 3 \rceil + \dots + \lceil \log_2 1000 \rceil\]and \[B =  \lfloor \log_2 2 \rfloor + \lfloor \log_2 3 \rfloor + \dots + \lfloor \log_2 1000 \rfloor.\]Compute $A-B.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
417c5846-3bd6-54bd-b040-361858e91111
task_key
intermediate~5falgebra--test--417c5846-3bd6-54bd-b040-361858e91111
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import