Academia Aeternum
तमसो मा ज्योतिर्गमय
Expand Any Power — All 36 Binomial Theorem Exercises Solved
2 exercise files · 20 total questions
\(T_{r+1} = {}^nC_r \cdot x^{n-r} \cdot y^r\)\(\text{Sum of coefficients: set }x=y=1 \Rightarrow 2^n\)\(\text{Middle term (n even): }T_{n/2+1}\)\(\text{Middle terms (n odd): }T_{(n+1)/2}\text{ and }T_{(n+3)/2}\)Step 1 — Write Tᵣ₊₁=ⁿCᵣ·xⁿ⁻ʳ·yʳ for every problem. Step 2 — Constant term (independent of x): set power of x=0, solve for r. Step 3 — Coefficient of xᵏ: set total power of x=k, solve r, substitute back. Step 4 — Greatest term: Tᵣ₊₁/Tᵣ≥1, solve r, verify with adjacent terms.
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