Question
Download Solution PDF\(\rm (2x - \frac {x} {2})^n\) के विस्तार के अंत से nवां पद क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
सामान्य पद: (x + y)n के विस्तार में सामान्य पद को निम्न द्वारा ज्ञात किया गया है
\(\rm {T_{\left( {r\; + \;1} \right)}} = {\;^n}{C_r} \times {x^{n - r}} \times {y^r}\)
(x + y)n के विस्तार में पदों की संख्या (n + 1) है।
अंत से (n + 1)वां पद पहला पद है और nवां पद दूसरा पद है।
गणना:
\(\rm (2x - \frac {x} {2})^n\) के विस्तार में एक विस्तार के अंत से nवां पद दूसरा पद है।
Tr+1 = nCr (2x)(n - r) \(\rm (\frac {-x} {2})^r\)
T2 = nC1.(2x)(n - 1) \(\rm (\frac {-x} {2})\)
= \(\rm - n \times 2^{(n - 1 - 1)} \times x^{(n - 1 +1)}\)
= \(\rm - n \times 2^{(n - 2)} \times x^{n}\)
= \(\rm - nx^n. 2^{(n - 2)}\)
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