Question
Download Solution PDFश्रृंखला \(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\) के पहले 20 पदों का योग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
1 से n तक के क्रमागत संख्याओं का योग:
\( \rm 1 + 2 + 3 +\ ...\ + n = \dfrac{n(n+1)}{2}\)
गणना:
दी गयी श्रृंखला में पहले 20 पदों के योग को निम्न रूप में लिखा जा सकता है:
\(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\)
\(\rm =\sqrt{5}+ 2\sqrt{5}+3\sqrt{5}+4\sqrt{5}+\ ...\ +20\sqrt5\)
\(\rm =\sqrt5(1+2+\ ...\ +20)\)
\(\rm =\sqrt5\times \dfrac{20\times21}{2}=210\sqrt5\)
Last updated on May 30, 2025
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