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One quick step with 8 * (2500 - 50) is to do the distributive operation: 8 * (2500 - 50) = 8 * 2500 - 8 * 50 = 20000 - 400 = 19600
@AbhijitBhattacharyajuКүн бұрын
It’s sum of geometric progression so S=a(r^n-1/r-1)=7*(7^5-1)/(7-1)=(7/6)*(49*49*7-1)=(7/6)*(7*(2500-100+1)-1) =(7/6)*(7*2401-1) =(7/6)*(16807-1) =(7/6)*(16806) =7*2801=19607
@Yurka-Shturka2 күн бұрын
This is the sum of a geometric progression
@fadetoblah28832 күн бұрын
I factored the original expression like so: 7³(7²+7+1+[1/7]+[1/7²]), and then proceeded with the following, fairly simple calculations... = 343(57+[56/343]) = 19551+56 = 19607
@TheChongsam4 күн бұрын
Starting from right to left, 7+49+49*7=343,..343*7,add these terms
@charlesmitchell58416 күн бұрын
Ok, good to know in case the calculator companies go out of business 😅.
@1291401632 күн бұрын
I came up with 19607 in my head 7^5 = 16807 7^4 = 2401, 16807 + 2401 = 19208 7^3 = 343, 19208 + 343 = 19551 7^2 = 49, 19551 + 49 = 19600 7^1 = 7, 19600 + 7 = 19607
I came up with the right answer with a lot less math.
@alestee42412 күн бұрын
8*49*50=4*49*100=(200-4)*100
@-datolith27756 күн бұрын
😀
@SpamtonSpamton-pm6hi5 күн бұрын
interesting, but so much slower than just summing the powers of 7
@rleroygordon3 күн бұрын
The problem is with trying to figure out powers of 7 in your head.
@SpamtonSpamton-pm6hi2 күн бұрын
@@rleroygordon yeah, but it just seems like using a lawnmower to cut a beard. by the time you figure out that relationship, you could've already calculated 7^4 as 2401 due to easy multiplication with 49^2. maybe if it was a sum with the largest term 7^8 or 7^10 i could understand. (and even then i'd use the finite geometric series formula instead as it uses way less operations than the other methods)