Use the formulas in your textbook to give an equivalent equa

Use the formulas in your textbook to give an equivalent equation without the summation. This is sometimes called the closed form of an equation. sigma_i = 0^N (5t^2 + i)

Solution

_{[i =0 to N]} (5i²+i)

=(5*0²+0)+_{[i =1 to N]} (5i²+i)

=0+_{[i =1 to N]} (5i²+i)

=_{[i =1 to N]} (5i²+i)

=_{[i =1 to N]} (5i²) +_{[i =1 to N]} i

=5_{[i =1 to N]}i² +_{[i =1 to N]} i

=5(N(N+1)(2N+1)/6) +(N(N+1)/2)

=(N(N+1)/2)((5(2N+1)/3) +1)

=(N(N+1)/2)(((10N+5)/3) +1)

=(N(N+1)/2)((10N+8)/3)

=N(N+1)((5N+4)/3)

=(1/3)N(N+1)(5N+4)