If n is a natural number , then n(n +1) (n +2) (n +3) +1 is always:
If n is a natural number , then n(n +1) (n +2) (n +3) +1 is always:
यदि n एक प्राकृतिक संख्या है, तो n(n +1) (n +2) (n +3) +1 हमेशा होगा:
Detailed Solution & Logic
Correct Answer:
A perfect square / एक पूर्ण वर्ग
The expression $n(n+1)(n+2)(n+3)+1$ can be rewritten as
$ n(n+3)(n+1)(n+2)+1 = (n^2+3n)(n^2+3n+2)+1 $.
Let $x = n^2 + 3n$.
Then the expression becomes
$ x(x+2)+1 = x^2 + 2x + 1 = (x+1)^2 $.
So, $n(n+1)(n+2)(n+3)+1$ is always a perfect square.
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