Mathematical Induction (MI) (Mission Impossible :S) (1 Viewer)

[wrxsti]

i dont even know how to begin thi question :S

Prove using Mathetmatical Induction that the sum of a geometric series is a(1-r^n)/(1-r)

 

[Mattamz]

ie Prove: a + ar + ar^2 .......+ar^(n-1) = a(1-r^n)/(1-r)

Test n =1:
LHS = a
RHS = a(1-r)/(1-r) = a

Assume n=k:
a + ar + ar^2 .......+ar^(k-1) = a(1-r^k)/(1-r)

Prove n=k+1:
a + ar + ar^2 .......+ar^(k-1) + ar^k
= a(1-r^k)/(1-r) +ar^k
=a(1-r^k)/(1-r) +ar^n(1-r)/(1-r)
=a(1-r^k + r^k - r^(k+1))/(1-r)
=a(1 - r^(k+1))/(1-r)

hence by the princple of mathematical induction true to all intergers n>=1