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