The sum of the fractions 1-2-1-6-1-12-1-20-1-30-1-42-1-56-1-72-1-90-1-110-1-132 is

The correct option is B 11/12 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132 =(1 1 / 2 )+( 1 / 2 1 / 3 )+( 1 / 3 1 / 4 )+( 1 / ...

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Byju's Answer

Standard VIII

Mathematics

Associative Property of Rational Numbers

The sum of th...

Question

The sum of the fractions $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132}$ is

\frac{7}{8}

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\frac{11}{12}

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\frac{15}{16}

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\frac{17}{18}

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Solution

The correct option is B $\frac{11}{12}$
$\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132}$
$= (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{7}) + (\frac{1}{7} - \frac{1}{8}) + (\frac{1}{8} - \frac{1}{9}) + (\frac{1}{9} - \frac{1}{10}) + (\frac{1}{10} - \frac{1}{11}) + (\frac{1}{11} - \frac{1}{12})$
$= (1 - \frac{1}{12})$
$= \frac{11}{12}$

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Similar questions

\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132}

is equal to:

\frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110}

is equal to : __.

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Q. Question 8 (ii)
The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

\begin{matrix} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 & 31 19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 & 2 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 & 3 12 & 14 & 2 & 9 & 6 & 15 & 15 & 7 & 6 & 12 \end{matrix}

What is the empirical probability that an engineer lives:
(ii) more than or equal to 7 km from her place of work?

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

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The sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132 is

The correct option is B 111212+16+112+120+130+142+156+172+190+1110+1132=(1−12)+(12−13)+(13−14)+(14−15)+(15−16)+(16−17)+(17−18)+(18−19)+(19−110)+(110−111)+(111−112)=(1−112)=1112

The sum of the fractions $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132}$ is