Show that \(n!>\left( \frac { n }{ e } \right) ^{ 2 }\) for n ∈ N

Find the middle term in \({ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }\)

Find the 5^th term in the sequence whose first three terms are 3, 3, 6 and each term after the second is the sum of the two terms preceding it.

Find the n^th term of the series 3 - 6 + 9 -12 + ...

In the binomial expansion of (1+a)^m+n, Prove  that the coefficients of a^m and aⁿ are equal.