Use the summation formulas to rewrite the expression without the summation notation.n4i + 5n2i = 1S(n) =

The expression you provided seems to be a bit unclear. However, if you're asking to rewrite a summation expression without the summation notation, here's a general approach using the formula for the sum of the first n natural numbers and the sum of the squares of the first n natural numbers.

The sum of the first n natural numbers is given by the formula:

S(n) = n*(n+1)/2

The sum of the squares of the first n natural numbers is given by the formula:

S(n^2) = n*(n+1)*(2n+1)/6

So if you have a summation like ∑(from i=1 to n) of (4i + 5i^2), you can rewrite it as:

4S(n) + 5S(n^2)

Substituting the formulas:

= 4*[n*(n+1)/2] + 5*[n*(n+1)*(2n+1)/6]

This is a general approach and you may need to adjust it based on your specific expression.