Q. 1 E5.0( 1 Vote )

Find the sum of the following series.52 + 72 + 92 + … + 392

Given the the series S = 52 + 72 + 92 + … + 392

Let S1 = 12 + 32

Let S2 = 22 + 42 + 62 + .. + 382 with n = 19

Let S3 = 12 + 22 + 32 + 42 + .. + 392 with n = 39

Required sum S = S3-S2-S1

To find the sum S1 -

S1 = 1 + 9 = 10

To find the sum S2

S2 can be rewritten as S2 = 22(12 + 22 + 32 + 42 + .. + 192)

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

S =

S2 =

=

=

S2 = 9880

To find the sum S3 -

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

S =

S3 =

=

= 20540

Required sum S = S3-S2-S1

S = 20540-9880-10 = 10650

The sum S = 52 + 72 + 92 + … + 392 = 10650

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 Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division Lemma49 mins
Fundamental Theorem of Arithmetic- 143 mins
Quiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 mins
Quiz | 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
view all courses