R=0}^{50}{{}^{50}{{C}_{r}}{{x}^{r}}}\]. Therefore, sum of COEFFICIENTS of odd power of x = \[{}^{50}{{C}_{1}}+{}^{50}{{C}_{3}}+...+{}^{50}{{C}_{49}}\] = \[\frac{1}{2}[{}^{50}{{C}_{0}}+{}^{50}{{C}_{1}}+...+{}^{50}{{C}_{50}}]\,\,=\,\,\frac{1}{2}[{{2}^{50}}]={{2}^{49}}\].

"> R=0}^{50}{{}^{50}{{C}_{r}}{{x}^{r}}}\]. Therefore, sum of COEFFICIENTS of odd power of x = \[{}^{50}{{C}_{1}}+{}^{50}{{C}_{3}}+...+{}^{50}{{C}_{49}}\] = \[\frac{1}{2}[{}^{50}{{C}_{0}}+{}^{50}{{C}_{1}}+...+{}^{50}{{C}_{50}}]\,\,=\,\,\frac{1}{2}[{{2}^{50}}]={{2}^{49}}\].

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In the expansion of \[{{(1+x)}^{50}},\] the sum of the coefficient of odd powers of x is [UPSEAT 2001; Pb. CET 2004]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 10 months ago

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We have, \[{{(1+x)}^{50}}=\sum\limits_{R=0}^{50}{{}^{50}{{C}_{r}}{{x}^{r}}}\]. Therefore, sum of COEFFICIENTS of odd power of x = \[{}^{50}{{C}_{1}}+{}^{50}{{C}_{3}}+...+{}^{50}{{C}_{49}}\] = \[\frac{1}{2}[{}^{50}{{C}_{0}}+{}^{50}{{C}_{1}}+...+{}^{50}{{C}_{50}}]\,\,=\,\,\frac{1}{2}[{{2}^{50}}]={{2}^{49}}\].

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Posted on 17 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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