12+16+112+120+12+16+112+120+\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + 130+142+156+172+" role="presentation">130+142+156+172+130+142+156+172+\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + 190+1110+1132=?" role="presentation">190+1110+1132=?190+1110+1132=?\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?" /> 12+16+112+120+12+16+112+120+\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + 130+142+156+172+" role="presentation">130+142+156+172+130+142+156+172+\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + 190+1110+1132=?" role="presentation">190+1110+1132=?190+1110+1132=?\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?" /> 12+16+112+120+12+16+112+120+\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + 130+142+156+172+" role="presentation">130+142+156+172+130+142+156+172+\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + 190+1110+1132=?" role="presentation">190+1110+1132=?190+1110+1132=?\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?" />

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Find the sum : $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} +$ $\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} +$ $\frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} +$ $\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} +$ $\frac{1}{90} + \frac{1}{110} + \frac{1}{132} = ?$ $\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?$

1 $\frac{7}{8}$ $\frac{7}{8}$
2 $\frac{11}{12}$ $\frac{{11}}{{12}}$
3 $\frac{11}{12}$ $\frac{{11}}{{12}}$
4 $\frac{17}{18}$ $\frac{{17}}{{18}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given expression, \\ = (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + . . . . . \\ + (\frac{1}{11} - \frac{1}{12}) \\ = (1 - \frac{1}{12}) \\ = \frac{11}{12} . \end{aligned}

$\eqalign{ & {\text{Given expression,}} \cr & {\text{ = }}\left( {1 - \frac{1}{2}} \right) + \left( {\frac{1}{2} - \frac{1}{3}} \right) + \left( {\frac{1}{3} - \frac{1}{4}} \right) + \left( {\frac{1}{4} - \frac{1}{5}} \right) + ..... \cr & \,\,\,\,\,\, + \left( {\frac{1}{{11}} - \frac{1}{{12}}} \right) \cr & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}}. \cr}$

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

$\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} +$

\frac{1}{90} + \frac{1}{110} + \frac{1}{132} = ?

$\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?$ ", "text": "Find the sum :

\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} +

$\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} +$

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

$\frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} +$

\frac{1}{90} + \frac{1}{110} + \frac{1}{132} = ?

$\frac{1}{{90}} + \frac{1}{{110}} + \frac{1}{{132}} = ?$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Given expression, \\ = (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + . . . . . \\ + (\frac{1}{11} - \frac{1}{12}) \\ = (1 - \frac{1}{12}) \\ = \frac{11}{12} . \end{aligned}

$\eqalign{ & {\text{Given expression,}} \cr & {\text{ = }}\left( {1 - \frac{1}{2}} \right) + \left( {\frac{1}{2} - \frac{1}{3}} \right) + \left( {\frac{1}{3} - \frac{1}{4}} \right) + \left( {\frac{1}{4} - \frac{1}{5}} \right) + ..... \cr & \,\,\,\,\,\, + \left( {\frac{1}{{11}} - \frac{1}{{12}}} \right) \cr & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}}. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Given expression, \\ = (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + . . . . . \\ + (\frac{1}{11} - \frac{1}{12}) \\ = (1 - \frac{1}{12}) \\ = \frac{11}{12} . \end{aligned}

$\eqalign{ & {\text{Given expression,}} \cr & {\text{ = }}\left( {1 - \frac{1}{2}} \right) + \left( {\frac{1}{2} - \frac{1}{3}} \right) + \left( {\frac{1}{3} - \frac{1}{4}} \right) + \left( {\frac{1}{4} - \frac{1}{5}} \right) + ..... \cr & \,\,\,\,\,\, + \left( {\frac{1}{{11}} - \frac{1}{{12}}} \right) \cr & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}}. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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