Question

Sum of series √2+√8+√18+√32.................

Answer 1

here the series formed is √2+2√2+3√2..........................

sn=n/2(2a+(n-1)d)

sn=n/2(2√2+(n-1)√2)

=n/2(√2+√2n)

=n/√2+n²/√2

Answer 2

$as \: we \: noted \: this \: series \: is \: in \: ap \\ a = \sqrt{2} \\ d = \sqrt{2} \\ so \: sn = \binom{n}{2} {2a + (n - 1)d} \\ sn = \binom{n}{2} {2( \sqrt{2} ) + (n - 1)( \sqrt{2}) } \\ sn = \binom{n}{2} { \sqrt{2} + \sqrt{2}n \: - \sqrt{2} } \\ so \: sn = \binom{ \sqrt{2}n}{2} \: \: \: \: \: is \: the \: right \: ans.$