Pascal's triangle nth triangular number [examples]

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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logic Idempotent law show x=xVx

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logic Idempotent law show x=xVx

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3rd/3ways: exp Derivative x^x

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3rd/3ways: exp Derivative x^x

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Find the number of permutations of the letters of the word ALLAHABAD

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Find the number of permutations of the letters of the word ALLAHABAD

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2nd way: derivative x w.r.t x^x. [YES, d(x)/d(x^x)!]

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2nd way: derivative x w.r.t x^x. [YES, d(x)/d(x^x)!]

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UC Davis: differentiate y=ln(cos^5(3x^4))

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UC Davis: differentiate y=ln(cos^5(3x^4))

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Overlord Movie 3: The Sacred Kingdom Sub English

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Screen Recording 2024-05-18 at 11.12.27 PM

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exp integral ∫a^x/b^x dx

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exp integral ∫a^x/b^x dx

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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【Shiny Watermelon】Sorry, Qingya, but it's really funny

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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1st way: trig derivative (sin(x))^x

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1st way: trig derivative (sin(x))^x

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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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2nd/2 ways: [k-map] logic:Simplify the Boolean function F=A+A'B

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2nd/2 ways: [k-map] logic:Simplify the Boolean function F=A+A'B

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3rd/3 ways: How many chords can be drawn through 21 points on a circle?

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3rd/3 ways: How many chords can be drawn through 21 points on a circle?

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

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If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

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