Prove by induction that the nth triangle number is given by n(n+1)/2
base case: (1 x 2)/2 = 1 as required inductive step: assuming statement holds for n=k, the (k+1)th triangle number is given by k(k+1)/2 + (k+1) by definition=(k^2+3k+2)/2=(k+1)(k+2)/2=(k+1)((k+1)+1)/2result follows by induction
CB
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Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4
Find the equation of the tangent to the curve x^3+yx^2=1 at the point (1,0).
x^3 + 3x^2 + 2x + 12