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PreviousUse mathematical induction to prove this formula for the sum of a finite number of terms of a geometric progression with initial term a and common ratio r: \sum_{j=0}^{n} ar^j = a + ar + ar^2 + \dots + ar^n = \frac{ar^{n+1} - a}{r-1} when $r e 1 where n$ is a non-negative integer.NextAn odd number of people stand in a yard at mutually distinct distances. At the same time each person throws a pie at their nearest neighbour, hitting this person. Use mathematical induction to show that there is at least one survivor, that is, at least one person who is not hit by a pie.