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Discussion

Mathematics Preparation for MCA Entrance

Ayesha (5)

The sum of n terms of the series $\frac{1}{1 \cdot 2 \cdot 3 \cdot 4} + \frac{1}{2 \cdot 3 \cdot 4 \cdot 5} + \frac{1}{3 \cdot 4 \cdot 5 \cdot 6} + \dots$ is

\frac{1}{3 (n + 1) (n + 2) (n + 3)}

\frac{1}{6 (n + 2) (n + 3) (n + 4)}

\frac{15}{4 n (n + 1) (n + 5)}

None of these

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Sanjay Maurya

Sanjay maurya

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Harsh Ranjan

By partial factorisation it can be resolved to

1/6 {1/(2) - 1/(n+1) + 1/(n+2) - 1/(n+3)}

Moreover if n tends to infinity than the answer becomes 1/12

Hence the correct option is (iv)

<SPAN style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri', 'sans-serif'; FONT-SIZE: 11pt; TOP: 10pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-text-raise: -10.0pt; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shape style="WIDTH: 96.75pt; HEIGHT: 22.5pt" id=_x0000_i1025 type="#_x0000_t75"> <v:imagedata chromakey="white" o:title="" src="file:///C:\Users\hemant\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"></v:imagedata></v:shape><?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p> By partial factorisation it can be resolved to 1/6 {1/(2) - 1/(n+1) + 1/(n+2) - 1/(n+3)} <SPAN style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri', 'sans-serif'; FONT-SIZE: 11pt; TOP: 10pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-text-raise: -10.0pt; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><v:shape style="WIDTH: 154.5pt; HEIGHT: 22.5pt" id=_x0000_i1025 type="#_x0000_t75"></v:shape> <SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri', 'sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><v:shape style="WIDTH: 138.75pt; HEIGHT: 27pt" id=_x0000_i1025 type="#_x0000_t75"><v:imagedata chromakey="white" o:title="" src="file:///C:\Users\hemant\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png"></v:imagedata></v:shape><o:p></o:p> Moreover if n tends to infinity than the answer becomes 1/12<o:p></o:p> Hence the correct option is (iv)<o:p></o:p> Please type your answer before submitting.

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Harsh Ranjan

By partial factorisation it can be resolved

to 1/6 {1/2 - 1/(n+1) + 1/(n+2) - 1/(n+3)

Moreover if n tends to infinity than the answer becomes 1/12

Hence the correct option is (iv)

<BLOCKQUOTE style="MARGIN-RIGHT: 0px" dir=ltr> <SPAN style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri', 'sans-serif'; FONT-SIZE: 11pt; TOP: 10pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-text-raise: -10.0pt; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shape style="WIDTH: 96.75pt; HEIGHT: 22.5pt" id=_x0000_i1025 type="#_x0000_t75"> <v:imagedata chromakey="white" o:title="" src="file:///C:\Users\hemant\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"></v:imagedata></v:shape><?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p> By partial factorisation it can be resolved <SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri', 'sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><v:shape style="WIDTH: 138.75pt; HEIGHT: 27pt" id=_x0000_i1025 type="#_x0000_t75"><v:imagedata chromakey="white" o:title="" src="file:///C:\Users\hemant\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png"></v:imagedata></v:shape><o:p>to 1/6 {1/2 - 1/(n+1) + 1/(n+2) - 1/(n+3)</o:p> Moreover if n tends to infinity than the answer becomes 1/12<o:p></o:p> Hence the correct option is (iv)<o:p></o:p> </BLOCKQUOTE> Please type your answer before submitting.

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