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Start the same way, but then note that it's a geometric series which has a well known formula. So the total is 8(8^5 - 1)/(8 - 1). 8^5 = 2^15 and powers of two are well known , so that can be written as (7 + 1)(32767)/7 = 32767 + 32767/7 = 32767 + 4681 = 37448.
Strange: the presented method doesn't seem easier than simply brute-forcing it: 2^10=1024, 2^5=32, so 2^15 = 1024*32, 2^12 = 1024*4, 2^9=512, 2^6 = 64, 2^3=8, so the entire question is: 1024*36 + 584, or (1000+24)*36 + 584 which is not harder than any of the calculations presented...
I was trying to figure out why the runtime of this video was so long when I figured it out in my head just from the thumbnail much faster than the length of this video. Now, after watching it, I see he took the long way around!! 😂😂 I just simply added each one as obvious powers of 2. 2^3 = 8 2^6 = 64 2^9 = 512 2^12 = 4096 2^15 = 32768 Thus, 32768 + 4096 + 512 + 64 + 8 = 37448 I just naturally went this way in my head without even thinking about any complicated maths solution. Why go complicated when simple will do? 😂
Exactly the way I would do it in my head. If I'm doing this on paper, I would set it up in a data table and then add the column. Works the same as what you showed, but the presentation looks a little different.
Other way: factor out 2^9 from the first three elements leads to : 2^9 (2^6 + 2^3 + 1) + 2^6 + 2^3 which is 512(72 + 1) + 72. This can also be written as 513 * 72 + 512 = which is 37488
Since at the end of the day there is going to be some arithmatic, another, and perhaps more modern way to think about this sum is to think of it as binary column values - so essentially you are converting 1001001001001000 to decimal. Powers of 2 are fairly easy to do in your head....
