Solve using principle of mathematical induction, prove that for every n >= 1, 7 + 13 + 19 + . . . + (6n + 1) = n (3n +4)
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Let P(n) denote the statement :
Put n=1,
L.H.S=7
R.H.S=3(1)+4=7
P(1) is true
Assume that P(k) is true
That is
7+13+19+.......+(6k+1)=k(3k+4) is true
To prove: P(k+1) is true
That is , to prove
is true
Now, consider
7+13+19+.......+(6k+7)
Thus, P(k+1) is true
Hence by mathematical induction P(n) is true for all natural numbers
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