Question

Use the method of Mathematical Induction to prove that, for every natural number n, the number n^2 + 5n + 6 is even.

Answer 1

first of all we will check for P(1) is it true or not??
for dat we will put n=1.luckily dat is true.....1+5+6 is divisible by 2


Now we will assume dat for P(K) this equation is true.......nd the equation is
K^2+5K+ 6 ----------equation no.1


Now we are going to try to prove dat dis equation is true for P(K+1)
for dat
(K+1)^2+5(K+1)+6
K^2+2k+1+5K+5+6
K^2+5K+6 + 2K+6
Now as we know dat K^2+5K+6 is divisible by 2
nd 2(k+3) is also divisible by
Therefore P(K+1) is satisfied
Hence Proved
Hope u get What m tryin to say