1 + 3 + 5 + + 99 1 + 3 + 5 + \ldots + 99

What is sum of all positive odd numbers from 1 to 100?


The answer is 2500.

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.

3 solutions

Hana Wehbi
Oct 1, 2017

0 49 ( 1 + 2 n ) = 0 49 ( 1 ) + 0 49 ( 2 n ) = 50 + 2 × 49 × 50 2 = 2500 \sum_0^{49}({1+2n}) = \sum_0^{49}(1)+ \sum_0^{49}(2n) = 50 + \frac{2\times49\times50}{2} = 2500

I have used the fact that 1 n k = n ( n + 1 ) 2 \sum_1^n{k} = \frac{n(n+1)}{2}

The sum of the first n odd numbers is aways equals to n^2 , 99 is the 50 odd number. So 50^2 = 2500

Let n be the nth odd number, then the sum is n^2. 99 is the 50th odd number so the answer is 2500.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...