Question
Download Solution PDFThe sum of the first 20 terms of the series \(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Sum of consecutive numbers from 1 to n: \( \rm 1 + 2 + 3 +\ ...\ + n = \dfrac{n(n+1)}{2}\).
Calculation:
The sum of the first 20 terms of the given series can be written as:
\(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\)
\(\rm =\sqrt{5}+ 2\sqrt{5}+3\sqrt{5}+4\sqrt{5}+\ ...\ +20\sqrt5\)
\(\rm =\sqrt5(1+2+\ ...\ +20)\)
\(\rm =\sqrt5\times \dfrac{20\times21}{2}=210\sqrt5\).
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