A Nice Olympiads Exponential Trick | No Calculator Allowed

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Пікірлер: 22

@shhi9379 5 ай бұрын

問題の計算=59049+6561+729+81+9=66429 (without calculator)

@aresyt5054 5 ай бұрын

It's a GP, so we can directly use the sum of a GP formula

@MATERémi 5 ай бұрын

And you can work out the result using no calculator ...?

@aresyt5054 5 ай бұрын

@@MATERémi yes , too easy

@-aqua-marine- 4 ай бұрын

Yep

@Prem-K007 4 ай бұрын

@@MATERémiyes , definitely only 9⁶ should be calculated which is nothing but (9³)² which is (729)² . Is it that much difficult to solve it with a pen and paper?. Using G.P formula =( 9⁶-9)/8 is the answer. Edit:- also you can do this for 9⁶ :- (730-1)²= (730)²+(1)²- 2(730)(1). Whole calculation can be done within 3 minutes

@coreymonsta7505 4 ай бұрын

It would probably be faster if he derived that formula then used it lmao

@coreymonsta7505 4 ай бұрын

at 2:00 you should just skip the middle two lines of work. And for (80 + 1)(80 + 2) technique was interesting, but you can just do 81*82 on paper in 10 seconds.

@0dd701 4 ай бұрын

+1 to the expression and then times (9-1) which is equal to 9^6-1, so the answer is (9^6-1)/(9-1)-1, or you can simply use the formula of sum of a geometric series.

@최정훈-i9b 4 ай бұрын

(9^6-9)÷8

@mmfpv4411 4 ай бұрын

Sum all the pascal triangle coefficients for (10-1)^n for n=1 to n=5 (sign alternates) then do the sum of powers of ten. Way faster

@МаксимЭлектрик-р3ы 4 ай бұрын

111110(9) =66429(10) 😅 Просто перевести девятиричную в десятиричную в столбик.

@mcichael9661 4 ай бұрын

It is extremely simpler and faster tocalculate the raised powers and just add the terms.

@kennethstevenson976 5 ай бұрын

I did the problem in 4 steps without the using of a variable using the distributive property.

@pspandey9737 5 ай бұрын

A simple sum in GP

@vanessawelles4760 5 ай бұрын

its actually easier/faster to simply do the addition by hand.

@gamer122333444455555 4 ай бұрын

Why did you add the extra steps of substituting 80 for X? The number is small enough and the math is short enough that in this case it was more efficient to directly foil the numbers rather than make it a algebra problem. There doesn't seem to be a need to generalize one problem in to an algebraic form.