Pascal's triangle grows row by row using the recurrence C(n,k) = C(n-1,k-1) + C(n-1,k), and this calculator reveals each step while keeping everything in BigInt. Beyond rows, it evaluates combinations directly, expands (ax + by)n, and verifies the classic identities involving 2n, alternating sums, and Lucas-derived odd counts.
Every run is designed for teaching: کاپی کریں a highlight-ready URL, drop the CSV log into slides, or use the narrated حساب کیسے کیا گیا pane to demonstrate the recurrence and binomial theorem live.
نتیجہ
حساب کیسے کیا گیا
Frequently asked questions
What limits apply to n and the expansion?
Rows are generated up to n = 200 for stability, and the binomial expansion is capped at n = 20 so coefficients remain readable. If you enter a larger value, the calculator shows a warning and safely clamps to those limits.
What appears in حساب کیسے کیا گیا?
Each run narrates the Pascal recurrence, the iterative C(n,k) formula, the binomial theorem, and the proofs of the row identities, so you can follow every step and export the log as CSV for lessons.