गणितीय आगमन सिद्धांत से सिद्ध कीजिए कि `(2n+7 )lt (n +3 )^(2 ),AA n in N.`

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

Prove the following (2 n + 7) lt (n + 3)^(2)

2 <= (1+ (1) / (n)) ^ (n) <3, n> = 1, n in N

By using the principle of mathematical induction , prove the follwing : P(n) : (2n + 7) lt (n+3)^2 , n in N

If n in N , then 3^(2n)+7 is divisible by

If n in N , then 3^(2n)+7 is divisible by

AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by