A 10sec problem

Algebra Level 2

Solve for n.

k = 3 n 2 3 k n 2 = 22 \sum_{k=3}^{n^2-3} \frac{k}{n^2}=22


The answer is 7.

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

k = 3 n 2 3 k n 2 = 22 \sum_{k=3}^{n^2-3} \frac{k}{n^2}=22

22 n 2 = l = 3 n 2 3 \Leftrightarrow 22n^2=\sum_{l=3}^{n^2-3}

22 n 2 = 1 2 ( n 2 3 ) ( n 2 2 ) 3 \Leftrightarrow 22n^2=\frac{1}{2}(n^2-3)(n^2-2)-3

44 n 2 = n 4 5 n 2 \Leftrightarrow 44n^2=n^4-5n^2

n = 7 \Leftrightarrow n=7

It took me like 15 seconds.

Adrian Neacșu - 7 years, 1 month ago

I couldn't understand transition from step 2 to 3

Shuvam Nayak - 7 years, 1 month ago

Log in to reply

Mr Meuris applied a formula for the sum of terms each of which is just 'k'. He replaced the beginning and ending values as appropriate.

Bill Bell - 6 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...