Q68. is equal to : limn→∞ (13+23+⋯⋯+n3)−(12+22+⋯⋯+n2) (1) 2 (2) 1 3 3 (3) 3 (4) 1 4 2
What This Question Tests
This problem requires replacing the sums of powers of natural numbers with their respective formulas and then evaluating the limit of the resulting rational polynomial as n approaches infinity.
Concepts Tested
Formulas Used
Σn = n(n+1)/2
Σn² = n(n+1)(2n+1)/6
Σn³ = [n(n+1)/2]²
📚 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.
13.2 — Obtain The Binding Energy Of The Nuclei 5626Fe And 20983 Bi In Units Of
Physics Class 12 · Chapter 13
13.2 Obtain the binding energy of the nuclei 5626Fe and 20983 Bi in units of MeV from the following data: m ( 5626Fe ) = 55.934939 u m ( 20983 Bi ) = 208.980388 u
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits involving summations
- Year
- 2024
- Shift
- 06 Apr Shift 2
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series; Class 12 Mathematics Ch 5: Continuity and Differentiability
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