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An equilateral triangle is divided into 36 smaller equilateral triangles by dividing each side into 6 parts and joining the corresponding points on adjacent sides of the triangle. *Image* There is a drunk ant at each of the 2 ...
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Let a1=0 and a2=1. an= n/2 an-1+ n/2 (n-1)an-2+(-1)n(1- n/2 ). Find f=an+2 nC2an-1 +3 nC3an-2+...+na1. ...
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Prove that there exists an irrational r for every natural number k(>=2) such that [rm]≡-1mod(k) for every natural number m. Here [x] is the greatest integer less than or equal to x. ...
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Try proving Lagrange's mean value theorem. ...
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Consider f(x)= ax2+bx+c, for |x|≤1. a,b,c are real numbers. If |f(x)| ≤1, find the maximum value of |2ax+b|. ...
