Purchase Solution

Several proofs by induction

Not what you're looking for?

Ask Custom Question

Show by induction that:

a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)]

b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)!

c) n^3+3n^2-10n is divisible by 3

d) 4^(2n+1) + 3^(n+2) is divisible by 13

See attached file for full problem description.

Attachments
Purchase this Solution

Solution Summary

The solution demonstrates the use of induction in proving mathematical identities.

Solution Preview

Please see the attached file.
Just for the record:
I had to change problem b.
It should read
Sum(r/(r+1)!) rather than Sum(r/(r-1)!). ...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts