Kamilmatematik100504idn
Answered

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Find the largest integer not greater than the following expression :
[tex]\displaystyle \large \boldsymbol{} \frac{2150}{2005} +\frac{2150}{2006} +\frac{2150}{2007 } + ...+\frac{2150}{2020}[/tex]

Sagot :

Mhanifaidn

Answer:

  • 17

Step-by-step explanation:

The number of terms:

  • 2020 - 2004 = 16

Each term is greater than 1, so the expression is greater than 16:

  • 2150/2005 = 1 + 145/2005
  • 2150/2006 = 1 + 144/2006
  • ...
  • 2150/2020 = 1 + 130/2020

It's easy to note each of the numbers getting smaller like 145/2005 > 144/2006 etc. Taking the smallest fraction.

The sum is:

  • S > 16 + 16*130/2020 = 16 + 2080/2020 > 16 + 1 = 17

So the largest integer not greater than S is 17.

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