Q82.Let {an}∞n=1 be a sequence such that a1 = 1, a2 = 1 and an+2 = 2an+1 + an for all n ≥1. Then the value of 47 ∑∞n=1( 23nan ) is equal to ________.
What This Question Tests
This question tests the ability to find the sum of an infinite series defined by a linear recurrence relation. It requires using either a closed-form solution for 'an' or, more efficiently, the concept of generating functions.
Concepts Tested
Formulas Used
Characteristic equation for recurrence relation: r² - 2r - 1 = 0
Generating function S = Σ(an * x^n)
📚 NCERT Sections This Tests
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
13.4 — Obtain Approximately The Ratio Of The Nuclear Radii Of The Gold Isotope
Physics Class 12 · Chapter 13
13.4 Obtain approximately the ratio of the nuclear radii of the gold isotope 197 79 Au and the silver isotope 10747 Ag .
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Recurrence relations and generating functions
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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