Q79.Suppose f is a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈N and f(1) = 51 . If ∑mn=1 n(n+1)(n+2)f(n) = 121 then m is equal to ______.
What This Question Tests
This problem involves solving a Cauchy functional equation, finding the general term of a series, and then calculating a summation using partial fractions.
Concepts Tested
Formulas Used
f(x+y) = f(x)+f(y) implies f(x)=cx
Summation formulas
📚 NCERT Sections This Tests
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.
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
1.4 — Concentrated Nitric Acid Used In Laboratory Work Is 68% Nitric Acid By Mass In
Chemistry Class 11 · Chapter 1
1.4 Concentrated nitric acid used in laboratory work is 68% nitric acid by mass in aqueous solution. What should be the molarity of such a sample of the acid if the density of the solution is 1.504 g mL–1? 27 Solutions Reprint 2025-26
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Functional equations and summation of series
- Year
- 2023
- Shift
- 29 Jan Shift 1
- Q Number
- Q79
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences & Series
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