Queen of the limit

Algebra Level 4

⌈ 1 2 ⌉ + ⌈ 1 2 + 1 100 ⌉ + ⌈ 1 2 + 2 100 ⌉ + ⌈ 1 2 + 3 100 ⌉ + . . . + ⌈ 1 2 + 299 100 ⌉ = ? \large{ \left\lceil \frac{1}{2} \right\rceil + \left\lceil \frac{1}{2} +\frac{1}{100}\right\rceil +\left\lceil \frac{1}{2} + \frac{2}{100}\right\rceil +\left\lceil \frac{1}{2} + \frac{3}{100} \right\rceil +...+\left\lceil \frac{1}{2} + \frac{299}{100} \right\rceil = \ ?}

Note: ⌈ x ⌉ \left\lceil x \right\rceil denotes the ceiling function, which is defined as the smallest integer that not less than x x .

Bonus : How did I name the problem?


The answer is 747.

View wiki
Hobart Pao by Hobart Pao , 23, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Aaaaa Bbbbb
Sep 27, 2015

Divide to range of the members based on numerator in each item of the given exp: 50 → 100 : 50 50 \rightarrow 100: 50 101 → 200 : 2 ∗ 100 101 \rightarrow 200: 2*100 201 → 300 : 3 ∗ 100 201 \rightarrow 300: 3*100 301 → 349 : 4 ∗ 49 301 \rightarrow 349: 4*49 So it is very easy to get the expression: R = 4 ∗ 49 + 500 + 51 = 747 R=4*49+500+51=\boxed{747}

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Pulkit Gupta
Dec 12, 2015

Solution is similar to the one already posted.

747 for Boeing 747 which is also known as the Queen of the Skies, hence the name :)

3 Helpful 0 Interesting 2 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...