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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
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2nd way: integral ∫ log √x(x^n) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction
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Purdue U: 2 ways Evaluate ∫2/(x (x-1)) dx where x=3 to 4
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NYU: 3 ways ∫(1+ln(x))/x dx
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prob stat: A die with 4 red faces & 2 green faces is rolled twice.
AP Calculus 2nd way: exp ∫1/(1+e^x) dx withOUT u-sub