Q54.If |x| < 1, |y| < 1 and x ≠1 , then the sum to infinity of the following series (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3)+. . . . . is (1) x+y−xy (2) x+y+xy (1+x)(1+y) (1+x)(1+y) (3) x+y−xy (4) x+y+xy (1−x)(1−y) (1−x)(1−y)
What This Question Tests
This question requires recognizing a pattern in a complex infinite series, simplifying each term using algebraic factorization, and then summing two resulting infinite geometric series.
Concepts Tested
Formulas Used
Σ a*r^(n-1) = a/(1-r) for |r|<1
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Sum of infinite series
- Year
- 2020
- Shift
- 02 Sep Shift 1
- Q Number
- Q54
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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