Q. 35.0( 1 Vote )

If 1 + 2 + 3 + … + p = 171, then find 13 + 23 + 33 + ... + p3.

Answer :

Given that the series S = 1 + 2 + 3 + … + p = 171


We have S =


p(p + 1) = 342


p2 + p = 342


Or p2 + p-342 = 0


Solving the quadratic using the quadratic formula



Where b = 1, a = 1, c = -342


We get,





p = is invalid because it yields a negative p which doesn’t make sense because number of terms in a series cannot be negative.


= 18


S = 13 + 23 + 33 + ... + p3 where p = 18


Formula to find the sum of first n cubes of natural numbers is


S =


S =


S =


S = 29241


The sum S = 13 + 23 + 33 + ... + p3 corresponds to p = 18 and S = 29241.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of Arithmetic41 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Euclids Division LemmaEuclids Division LemmaEuclids Division Lemma49 mins
NCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Quiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real Numbers37 mins
Relation Between LCM , HCF and NumbersRelation Between LCM , HCF and NumbersRelation Between LCM , HCF and Numbers46 mins
Application of Euclids Division LemmaApplication of Euclids Division LemmaApplication of Euclids Division Lemma50 mins
Quiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of Arithmetic51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses