Series Binomial Theorem Limits Worksheet

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Precalculus Math Worksheets – Mathbot, the Math Made Easy robot coach, with free printable worksheets for Precalculus

These problems cover sigma notation, arithmetic and geometric series, infinite geometric series, the binomial theorem with Pascal’s triangle, and informal limits of sequences and functions (A-APR.C.5, A-SSE.B.4 and F-BF.A.2).
The last problems use theater seating, savings, a bouncing ball and medicine doses.

Standards: A-APR.C.5, A-SSE.B.4, F-BF.A.2 · Level: Grade 12 Precalculus

Problem 1 Evaluating a Sum ★★★

Evaluate ∑_k=1⁶ (k² + 1).

Problem 2 Writing Sigma Notation ★★★

Write 4 + 7 + 10 + 13 + 16 in sigma notation.

Problem 3 An Arithmetic Series ★★★

Find the sum 7 + 11 + 15 + … + 51.

Problem 4 A Geometric Series ★★★

Add up the first seven terms of the geometric sequence that begins 4, 12, 36, and so on. Use the sum formula.

Problem 5 An Infinite Sum ★★★

Partial sums of the series.

The chart shows the partial sums of 9 + 6 + 4 + 83 + …. Find the sum of the series.

Problem 6 Divergent or Not? ★★★

Does 8 + 9.6 + 11.52 + … have a sum? Explain.

Problem 7 How Many Terms? ★★★

An arithmetic series has first term −4 and common difference 3. Its sum is 217. Find the number of terms.

Problem 8 An Alternating Sum ★★★

Evaluate ∑_k=1⁷ 5(−2)^k−1.

Problem 9 A Repeating Decimal ★★★

Write 0.272727… as an infinite geometric series and find the fraction it equals.

Problem 10 An Alternating Infinite Series ★★★

Find ∑_k=1^∞ 6(−12)^k−1.

Problem 11 Pascal’s Triangle Expansion ★★★

Pascal triangle, rows 0 to 5.

Use row 5 of Pascal’s triangle to expand (x + 2)⁵.

Problem 12 Expanding with a Coefficient ★★★

Expand (2x − 3)⁴.

Problem 13 A Single Coefficient ★★★

Find the coefficient of x³ in the expansion of (x + 4)⁷.

Problem 14 A Limit from a Table ★★★

The graph of f(x) = (x² − 9)/(x − 3).

Let f(x) = x² − 9x − 3. (a) Complete the table of values. (b) Find lim_x→3 f(x) and explain why f(3) does not exist.

x	2.9	2.99	2.999	3.001	3.01
f(x)	?	?	?	?	?

Problem 15 Theater Seating ★★★

A theater has 18 rows. The first row has 14 seats and each row after it has 2 more seats than the row before. (a) How many seats are in row 18? (b) How many seats are there in all?

Problem 16 Monthly Savings Plan ★★★

A student deposits $40 in month 1 and increases each month’s deposit by 5% over the previous month, for 24 months. Find the total deposited, to the nearest cent.

Problem 17 Bouncing Ball ★★★

A bouncing ball: each rebound is 70% as high as the last.

A ball is dropped from 10 feet. After each bounce it rises to 70% of the height of the previous fall. Find the total distance it travels before it comes to rest, to the nearest hundredth.

Problem 18 Medicine Dosage ★★★

A patient takes a 200 mg dose each morning. By the next morning, 30% of the drug from the previous day is still in the body. (a) Find the amount in the body right after the first, second and third doses. (b) Find the long-run amount right after a dose.

Problem 19 A Special Term ★★★

In the expansion of (x² + 1x)⁶, find (a) the constant term and (b) the coefficient of x³.

Problem 20 Limits of a Function and a Sequence ★★★

Find (a) lim_x→−1 x³ + 1x + 1 and (b) lim_n→∞ 6n² + 52n² − n + 3. (c) Explain why part (a) can have a limit even though the expression is undefined at x = −1.

Series Binomial Theorem Limits lesson Series Binomial Theorem Limits test Series Binomial Theorem Limits quiz

Mis à jour le 22 October 2026