The sum of the first 20 terms of the series \(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\) is:

Question

Question

Answer 1

Concept:

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:

\(\rm \sqrt{5}+ \sqrt{20}+\sqrt{45}+\sqrt{80}+\ ...\)

\(\rm =\sqrt{5}+ 2\sqrt{5}+3\sqrt{5}+4\sqrt{5}+\ ...\ +20\sqrt5\)

\(\rm =\sqrt5(1+2+\ ...\ +20)\)

\(\rm =\sqrt5\times \dfrac{20\times21}{2}=210\sqrt5\).