Question
Download Solution PDFजहाँ i = √-1 दिया गया है, तो योग \(\rm \Sigma_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
माना कि I = \(\rm \Sigma_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})\)
⇒ I = \(\rm \Sigma_{n=1}^{20}(i^n (\frac{1}{i} +1+ i)\)
⇒ I = \(\rm \Sigma_{n=1}^{20}(i^n (1)\)
⇒ I = \(i^1+ i^2+i^3+i^4+i^5+........+ i^{20}\)
⇒ I = \(5.(i^1+ i^2+i^3+i^4) = 0\) ( {∵ i + i2 + i3 + i4 = 0} )
∴ विकल्प (b) सही है।
Last updated on May 30, 2025
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