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Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.

Continue the two sequences of numbers below and find an equation to each of the sequences: n 1 2 3 4 5 6 7 Equation an 2 5 9 14 20 27 bn 1 3 12 60 360 2520 

Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.

"Question1\n\nGiven A= [\u25a0(2&2&1@1&3&1@1&2&2)] \n\n\n\n\n1.1 find the eigenvalues of A\n\n1.2. Determine an eigenvector for the eigenvalue = 5\n\n\n\nQuestion2\nA periodic function f(x) with period 2 \u03c0 is defined by :\n f(x)= [ (x+\u03c0)\/2 -\u03c0\u02c2 X\u02c2 0, (x-\u03c0)\/2 0\u02c2 X\u02c2 \u03c0]\n\nDetermine the Fourier series for the periodic function"

Consider 3 distinct points M₁, M₂, and M₃ with respective affixes z₁, z₂, and z₃. Show that (Triangle M₁, M₂, and M₃ is equilateral) ↔ ( z₁² + z₂² +z₃² - z₁z₂ - z₂z₃ - z₁z₃).

Express 2x/ x²-1 in partial fractions and hence find the general solution of the differential equation dy/dx = 2xy / x² - 1 expressing y explicitly in terms of x.