Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 14
What is the sum of the following series: $$ \frac{1}{1 \times 2} + \frac{1}{2 \times 3}+\frac {1}{3 \times 4}$$ ....... $$+ \frac{1}{100 \times 101}$$?
Solution
Given series can be written as:
$$\sum_{n=1}^{100} (\frac{1}{n\times (n+1)})$$
or $$\sum_{n=1}^{100} (\frac{(n+1)-n}{n\times (n+1)})$$
or $$\sum_{n=1}^{100} (\frac{1}{n} - \frac{1}{n+1})$$
After putting values of n from 1 to 100, all terms will cancel out, only first and last terms will be there
i.e. $$1-\frac{1}{101}$$
or $$\frac{100}{101}$$
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 38+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Logarithms, Surds and Indices QuestionsCAT Remainders QuestionsCAT Arithmetic QuestionsCAT Inequalities QuestionsCAT Simple Interest Compound Interest Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Special Charts QuestionsCAT DI with connected data sets QuestionsCAT Coins and Weights QuestionsCAT Charts QuestionsCAT Arrangement Questions
