summation rules

Question

Evaluate the following Sum, using standard summation formulas.

(n)

E (5i^2+4i)

I=1

Hint: Your answer should be a function of 𝑛.This list of summation rules may be helpful.

Answer 1

∑ⁿ_i=1 (5i²+4i)

= (∑ⁿ_i=1 5i²) + (∑ⁿ_i=1 4i)

= 5(∑ⁿ_i=1 i²) + 4(∑ⁿ_i=1 i)

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

= 5n(2n²+3n+1)/6 + 2n(n+1)

= (10n³+15n²+5n)/6 + 2n²+2n

= (5/3)n³+(5/2)n²+(5/6)n+2n²+2n

= (5/3)n³+(9/2)n²+(17/6)n

Hope this helped!