For a positive integer $n$, consider $$n(n+1)(n+2)(n+3)+1.$$ Calculate the expression for $n=1$

Question

For a positive integer $n$, consider $$n(n+1)(n+2)(n+3)+1.$$ Calculate the expression for $n=1$ and $n=2$. Prove that the expression is always a perfect square. Hint: group $n(n+3)$ and $(n+1)(n+2)$, then let $t=n^2+3n$.

Accepted Answer

(a) $25,121$; (b) $(n^2+3n+1)^2$.

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

Solution:

Solution locked