<p>I was practicing until I came across this problem from a QAS, I do not know how to do this fast. Can anyone tell me?
For all positive integers a, let #a# be defined as the sum of the odd integers from 0 to a, inclusive. For example, #8# = 1 + 3 + 5 + 7 = 16. What is the value of #100# - #96#?</p>
<h1>100# = (1+3+…+95+97+99)</h1>
<h1>96# = (1+3+…95)</h1>
<p>If you compare the sets, the first only has two extra elements - 97 and 99. Therefore the sum of those minus 0 would be the answer. </p>
<p>Ans: 196</p>
<p>It’s asking you for the difference. Think about it: what is a “difference”? Between 100 and 96, there are only two odd numbers—97, and 99.</p>
<p>The answer is 97 + 99 = 196.</p>
<h1>96# goes all the way up to 95 (the highest odd number from 0 to 96)</h1>
<h1>100# goes all the way up to 99 (the highest odd number from 0 to 100)</h1>
<h1>100# includes #96# (which ends at 95). So, it continues on to 97, then 99.</h1>
<p>97 + 99 = 196</p>
<p>Essentially:</p>
<h1>96# = [1+3+5+7+…+91+93+95]</h1>
<h1>100#=[1+3+5+7+…+91+93+95+97+99]</h1>
<p>When you subtract, the bold numbers cancel out</p>
<p>Oh okay, I understand now. Thanks a lot. I guess you just have to think about it very broadly then you understand</p>