Problems on Mathematical Induction
Mathematical Induction
For all n >= 1, prove that
12+22+32+42+.....+n2 = n(n+1)(2n+1)/6
For every positive integer n
13+23+33+43+.....+n3 = (n(n+1)/2 )2
For every positive integer n, prove that 7n-3n is divisible by 4.
Show that (2.7n+3.5n-5) is divisible by 24.
Prove that
102n-1+1 is divisible by 11
x2n-y2n is divisible by (x+y)
32n+2-8n-9 is divisible by 8
41n-14n is a multiple of 27
n(n+1)(n+5) is a multiple of 3
Using mathematical induction, prove that
a+ar+ar2+ar3+ar4....arn-1 = a(rn-1)/(r-1)
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Problems on mathematical induction. If you need solution to these problems, contact k1kumar@yahoo.com
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