# Find the sum of first n terms of the series(i) 7 + 77 + 777 + … . (ii) 0.4 + 0.94 + 0.994 + … .

(i) Series = 7 + 77 + 777 + …..n terms

Series = [9×(1 + 11 + 111 + …..)] ( Multiplying and dividing by 9)

Series = [9 + 99 + 999 + …..]

Series = [(10–1) + (100–1) + (1000–1) + …..]

Series = [10 + 100 + 1000 + ….. – (n×1)]

Series = [10 + 100 + 1000 + …..] – We find the sum of 10 + 100 + 1000…..n terms as:

First term = 10

Common ratio = = 10

Sum of n terms = Sum of n terms = Sum of n terms = Series = [ ] – Series =  (ii) Series = 0.4 + 0.94 + 0.994 + …..n terms

Series = (1–0.6) + (1–0.06) + (1–0.006) + ……..

Series = n×1 – (0.6 + 0.06 + 0.006 + ….)

We find the sum of 0.6 + 0.06 + 0.006…..n terms as:

First term = 0.6

Common ratio = = Sum of n terms = Sum of n terms = Sum of n terms = Series = n – 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  Fundamental Theorem of Arithmetic- 143 mins  Quiz | Imp Qs on Real Numbers37 mins  Euclids Division Lemma49 mins  NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins  Relation Between LCM , HCF and Numbers46 mins  Application of Euclids Division Lemma50 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 