Mathematical Induction

n
Σ =
r = 1
You can specify expressions using:
+ , - , * , / , sq( ) , cube( ), power( , ) , factorial( ), exp( ), ln( )

Exercises for students:
Prove the following by induction and check your working using the above application:

n
Σ 2*r - 1 = sq(n)
r=1

n
Σ sq(r) = n*(n+1)*(2*n+1)/6
r=1

n
Σ cube(r) = sq(n)*sq(n+1)/4
r=1

n
Σ power(2,r-1) = power(2,n) - 1
r=1

n
Σ r*factorial(r) = factorial(n+1) - 1
r=1

n
Σ (sq(r)+1)*factorial(r) = n*factorial(n+1)
r=1

n
Σ r*(r-1) = n*(sq(n) - 1)/3
r=1

n
Σ r*(r+4) = n*(n+1)*(2*n+13)/6
r=1



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