sum from n equals 1 to 2 m of cap A sub n equals the fraction with numerator 1 open paren 2 close paren and denominator 2 end-fraction minus the fraction with numerator 2 open paren 3 close paren and denominator 2 end-fraction plus the fraction with numerator 3 open paren 4 close paren and denominator 2 end-fraction minus the fraction with numerator 4 open paren 5 close paren and denominator 2 end-fraction plus … minus the fraction with numerator 2 m open paren 2 m plus 1 close paren and denominator 2 end-fraction
Find the equation of the circle with centre (2, -3) passing through (5, 1). 1990-hl-gen maths 05
Ak+1=(-1)k(k+1)(k+2)2cap A sub k plus 1 end-sub equals open paren negative 1 close paren to the k-th power the fraction with numerator open paren k plus 1 close paren open paren k plus 2 close paren and denominator 2 end-fraction Starting with the definition of Ak+1cap A sub k plus 1 end-sub sum from n equals 1 to 2 m
Advanced trigonometry and coordinate geometry. The Anatomy of Question 05 Ak+1=(-1)k(k+1)[(k+1)−k2]cap A sub k plus 1 end-sub equals
A heavy focus on the "Prove by Induction" method.
Ak+1=(-1)k(k+1)[(k+1)−k2]cap A sub k plus 1 end-sub equals open paren negative 1 close paren to the k-th power open paren k plus 1 close paren open bracket open paren k plus 1 close paren minus k over 2 end-fraction close bracket