An algebra problem by st ramanujan

Algebra Level 2

What is the sum of all positive integers n n satisfying 3 ≤ n ≤ 99 \sqrt3 \leq n \leq \sqrt{99} ?

44 76 284 900 275

St Ramanujan by st ramanujan , 40, India

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.

1 solution

3 = 1.732 , 99 = 9.94. ∴ The integers lying between those two irrational numbers are 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9. ∴ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ( ∑ n = 1 9 n ) − 1 ⟹ 45 − 1 = 44 . \large \displaystyle \sqrt{3} = 1.732, \sqrt{99} = 9.94.\\ \large \displaystyle \therefore \text{The integers lying between those two irrational numbers are } 2,3,4,5,6,7,8,9.\\ \large \displaystyle \therefore 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = \left( \sum_{n=1}^9 n \right) - 1 \\ \large \displaystyle \implies 45 - 1 = \color{#20A900}{\boxed{44}}.

8 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...