Show that `1!+2!+3!++n !` cannot be a perfect square for any `n in N ,ngeq4.`

Show that 9^n cannot end with the digit 2 for any n in N .

Show that 12^(n) cannot end with the digits 0 or 5 for any natural number n

Show that n!(n+2)=n!+(n+1)!

Perfect square or square number A natural number n is called a perfect square or a square number if there exists a natural number m such that n=m^(2)

if n is the smallest natural number such that n+2n+3n+* * * * * * *+99n is a perfect squre , then the number of digits in n^(2) is -

If n is the smallest natural number such that n+2n+3n+...+99n is a perfect square, then the number of digits in n^(2) is

The square root of a perfect square containing n digits has dots...... digits.

The square root of a perfect square of n digits will have n/2 digits if n is even.

Suppose n is a positive integer such that (n^2 + 48) is a perfect square. What is the number of such n? (n<5)