LEARN · EXPLAIN · REVISE

Find the sum of all coefficients of (2+x)^m.

Read the idea, work independently, then explain what changed.

高三選擇性必修第三册(A版).pdf · 6.3 · PDF 34 / printed page 29

TOPIC 01

Binomial theorem

Use the general term to locate coefficients, constants and coefficient sums.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

m=11

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Decide whether choices are alternative cases or successive stages, then check overlap.

Hint 2

Substitute x=1.

Worked solution

Decide whether choices are alternative cases or successive stages, then check overlap.
Apply the stated relation and retain its conditions.
$(2+1)^{11}=177147$
Use x=1 for the full coefficient sum, not 2^m unless both base coefficients equal one.

The requested value is 177147.

Checks and common pitfalls: Use x=1 for the full coefficient sum, not 2^m unless both base coefficients equal one.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Defining relation: Use the general term to locate coefficients, constants and coefficient sums.
$(a+b)^n=\sum_{r=0}^nC_n^ra^{n-r}b^r$
Conditions: The exponent n is a nonnegative integer; term number is r+1, not r.