What is the value of 999 frac{1}{2} + 999 fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The given expression is $999 \frac{1}{2} + 999 \frac{1}{6} + 999 \frac{1}{12} + 999 \frac{1}{20} + 999 \frac{1}{30}$.This can be written as $(999

Vedclass · Accepted Answer

$4995 \frac{5}{6}$

Vedclass · Answer

(D) The given expression is $999 \frac{1}{2} + 999 \frac{1}{6} + 999 \frac{1}{12} + 999 \frac{1}{20} + 999 \frac{1}{30}$.This can be written as $(999 + \frac{1}{2}) + (999 + \frac{1}{6}) + (999 + \frac{1}{12}) + (999 + \frac{1}{20}) + (999 + \frac{1}{30})$.Grouping the whole numbers and fractions: $(999 	imes 5) + (\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30})$.$999 	imes 5 = 4995$.Now,sum the fractions: $\frac{1}{1 	imes 2} + \frac{1}{2 	imes 3} + \frac{1}{3 	imes 4} + \frac{1}{4 	imes 5} + \frac{1}{5 	imes 6}$.Using the formula $\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$,we get: $(1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6})$.This simplifies to $1 - \frac{1}{6} = \frac{5}{6}$.Therefore,the total value is $4995 + \frac{5}{6} = 4995 \frac{5}{6}$.

What is the value of $999 \frac{1}{2} + 999 \frac{1}{6} + 999 \frac{1}{12} + 999 \frac{1}{20} + 999 \frac{1}{30}$?

Similar Questions

If $x=2$,then find the value of $x^{3}+27x^{2}+243x+631$.

$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28}$ is equal to

Between two fractions $\frac{1}{2}$ and $\frac{1}{8},$ how many fractions are there in all?

If $x = \frac{4 \sqrt{ab}}{\sqrt{a} + \sqrt{b}}$,then what is the value of $\frac{x + 2 \sqrt{a}}{x - 2 \sqrt{a}} + \frac{x + 2 \sqrt{b}}{x - 2 \sqrt{b}}$ (when $a \neq b$)?

The difference between two numbers is $9$ and the difference between their squares is $207$. The numbers are

Vedclass Test Series

Exam Paper Generator

Online Exam Module