Question

Calculate S3, S4, and S5 and then find the sum Σ using the identity n=1 1 1 1 47²-9 = = (2-3-20²+3) 62n 2n (Give an exact answer. Use symbolic notation and fractions where needed.) S3 = S4= Incorrect S5 = Incorrect 19 945 1 4n² - 9 178 10395 839 135135 I

Answer 1

To find S3, S4, and S5, substitute the values of n into the expression and simplify. The sum Σ can be found using the identity n² and substituting the value of n into the expression.

Step-by-step explanation:

The expression in the box is equal to n². To find S3, S4, and S5, we can substitute the values of n into the expression and simplify:

S3 = 2[1 + (3-1) + 3] = 2[1+2+3] = 2(6) = 12

S4 = 2[1 + (4-1) + 3 + (4-3)] = 2[1+3+3+1] = 2(8) = 16

S5 = 2[1 + (5-1) + 3 + (5-3) + (5-3)] = 2[1+4+3+2+2] = 2(12) = 24

To find the sum Σ, we can use the identity n² and substitute the value of n into the expression: Σ = 2n² = 2(5²) = 2(25) = 50