Integers Between 100 and 1000 With Digit Sum Equal to 14
Count the 3-digit integers between 100 and 1000 whose digits sum to 14, using stars-and-bars with inclusion-exclusion for the digit-range constraints.
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f(x)=2x/√(1+9x²) Composed 10 Times, Find √(3α+1)
Consider f:R→R defined by f(x)=2x/√(1+9x²). If (f∘f∘⋯∘f, 10 times)(x)=2^10x/√(1+9αx²), find the value of √(3α+1).
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Roots of x²−√2x−√3=0, Pn=αⁿ−βⁿ, Find (11√3−10√2)P10+(11√2+10)P11−11P12
Let α, β (α>β) be roots of x²−√2x−√3=0 and Pn=αⁿ−βⁿ. Find (11√3−10√2)P10+(11√2+10)P11−11P12 using the Newton recurrence for power sums.