# Several proofs by induction

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.

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#### 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)!). ...

#### Solution Summary

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

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