Sequences and Series Class 11 Maths Notes – Formulas & Quick Revision

Sequences and Series mein AP, GP aur special series ke sum formulas aate hain — scoring aur concept dono. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Sequences and Series

• AP: aₙ = a + (n−1)d; Sₙ = n/2[2a + (n−1)d] = n/2(a + l)
• AM: A = (a+b)/2
• GP: aₙ = arⁿ⁻¹; Sₙ = a(rⁿ−1)/(r−1)
• Infinite GP: S∞ = a/(1−r), |r| < 1
• GM: G = √(ab); AM ≥ GM
• Σn = n(n+1)/2
• Σn² = n(n+1)(2n+1)/6
• Σn³ = [n(n+1)/2]²

Quick Revision Points

• AP ke 3 terms: a−d, a, a+d lo (sum diya ho to)
• GP ke 3 terms: a/r, a, ar
• AM ≥ GM inequality JEE mein use hoti hai
• Sₙ − Sₙ₋₁ = aₙ — nth term nikalne ka trick
• Special series ke sums directly lagte hain

FAQ

AP-GP mixed questions kaise karu?

PDF mein AGP ka method + solved examples hain — pattern fix hai.

S∞ kab exist karta hai?

Sirf |r| < 1 ho tab — warna series diverge karti hai.

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