Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
19.8k views
in Number System by (46.2k points)
closed by

What is the value of \(\frac34+\frac5{36}+\frac7{144}+........+\frac{17}{5184}+\frac{19}{8100} ?\)

(a) 0.95 

(b) 1 

(c) 0.99 

(d) 0.98

1 Answer

+1 vote
by (49.2k points)
selected by
 
Best answer

(c) 0.99

\(\frac34+\frac5{36}+\frac7{144}+........+\frac{17}{5184}+\frac{19}{8100} \)

\(\frac{3}{1^2.2^2}\) + \(\frac{5}{2^2.3^2}\) + \(\frac{7}{4^2.3^2}\) + ........ + \(\frac{17}{8^2.9^2}\) + \(\frac{19}{9^2.10^2}\)

\(\big(1-\frac1{2^2}\big) + \big(\frac1{2^2}-\frac1{3^2}\big) + \big(\frac1{3^2}-\frac1{4^2}\big) + ...... +\big(\frac{1}{8^2}-\frac1{9^2}\big) + \big(\frac{1}{9^2}-\frac1{10^2}\big)\)

= 1 - \(\frac1{10^2}\) = 1 - \(\frac1{100} = \frac{99}{100}\) = 0.99.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...