Sequences, Limits and Series — Classroom Resources

Open with ¼ + 1/16 + 1/64 + … = ⅓ — Infinity at a Glance. Ask students what they notice and what question the resource raises before introducing the formal idea.

Let students explore Odd Numbers Sum to a Square (1+3+5+…=n²), then ask them to describe the pattern, argument, or representation in their own words.

Let students explore Triangular Numbers: 1+2+…+n = n(n+1)/2, then ask them to describe the pattern, argument, or representation in their own words.

Let students explore Infinite Series, then ask them to describe the pattern, argument, or representation in their own words.

Use Limit and Continuity as an extension or assignment that connects the lesson to a broader mathematical story.

Use Cantor's Infinity — What He Saw But Did Not Believe as an extension or assignment that connects the lesson to a broader mathematical story.

Use The Birth of Transfinite Numbers as an extension or assignment that connects the lesson to a broader mathematical story.