Questions from General Calculus

Q: Write the sum in sigma notation. 1 + 2 +

Write the sum in sigma notation. 1 + 2 + 4 + 8 + 16 + 32

Q: Write the sum in sigma notation. 1/1 +

Write the sum in sigma notation. 1/1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36

Q: Write the sum in sigma notation. x + x2 +

Write the sum in sigma notation. x + x2 + x3 + … + xn

Q: Write the sum in expanded form. ∑6i=1

Write the sum in expanded form. ∑6i=1 1/i +1

Q: Write the sum in sigma notation. 1 – x +

Write the sum in sigma notation. 1 – x + x2 – x3 + … + (-1)n xn

Q: Find the value of the sum. ∑8i=4

Find the value of the sum. ∑8i=4 (3i – 2)

Q: Find the value of the sum. ∑6i=3

Find the value of the sum. ∑6i=3 i(i + 2)

Q: Suppose that F, G and Q are polynomials and F (

Suppose that F, G and Q are polynomials and F (x)/ Q (x) = G (x)/ Q (x) for all x except when Q (x) = 0. Prove that F (x) = G (x) for all x. [Hint: Use continuity.]

Q: Find the value of the sum. ∑6j=4

Find the value of the sum. ∑6j=4 3i + 1

Q: Find the value of the sum. ∑8k=0

Find the value of the sum. ∑8k=0 cos kπ