Questions from General Calculus

Q: Evaluate each telescoping sum. (a). ∑n i

Evaluate each telescoping sum. (a). ∑n i=1 [i4 – (i – 1)4]

Q: Prove the generalized triangle inequality: |∑ n i=

Prove the generalized triangle inequality: |∑ n i=1 ai| < ∑n i=1 |ai|

Q: Write the sum in expanded form. ∑4k=1

Write the sum in expanded form. ∑4k=1 2k – 1/ 2k + 1

Q: Write the sum in expanded form. ∑8k=5

Write the sum in expanded form. ∑8k=5 xk

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

Write the sum in expanded form. ∑ni=1 i10

Q: Write the sum in expanded form. ∑n+3j

Write the sum in expanded form. ∑n+3j=n j2

Q: Write out the form of the partial fraction decomposition of the function

Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.

Q: Evaluate the integral. f 1/(t – 4)

Evaluate the integral. f 1/(t – 4) (t – 1), dt

Q: Evaluate the integral. f32 1/x2 – 1,

Evaluate the integral. f32 1/x2 – 1, dx

Q: Evaluate the integral. f10 x - 1/x2 +

Evaluate the integral. f10 x - 1/x2 + 3x + 2, dx