Q82.If ∑10r=1 r!(r3 + 6r2 + 2r + 5) = α(11!), then the value of α is equal to ___ .
What This Question Tests
This question tests the ability to algebraically manipulate an expression involving factorials to convert it into a telescoping sum. It requires recognizing and simplifying r!(r^3 + 6r^2 + 2r + 5) into the form (r+3)! - (r-1)!.
Concepts Tested
Formulas Used
∑ [ f(r+1) - f(r) ] = f(N+1) - f(1)
r! (r+1) = (r+1)!
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
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.
8.2 — Name The Following Compounds According To Iupac System Of Nomenclature:
Chemistry Class 12 · Chapter 8
8.2 Name the following compounds according to IUPAC system of nomenclature: (i) CH3CH(CH3)CH2CH2CHO (ii) CH3CH2COCH(C2H5)CH2CH2Cl (iii) CH3CH=CHCHO (iv) CH3COCH2COCH3 (v) CH3CH(CH3)CH2C(CH3)2COCH3 (vi) (CH3)3CCH2COOH (vii) OHCC6H4CHO-p
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Summation of series involving factorials
- Year
- 2021
- Shift
- 18 Mar Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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