Answer:

√2.n.(n+1)/2

Step-by-step explanation:

the series is

√2+√8+√18+√32...

=√2+2√2+3√2+4√2

here the 1st term is √2 and common difference is (2√2+√2)=√2

so,sum of the n th term is

n/2{2.1st term+(n-1).common difference}

=n/2{2.√2+(n-1).√2}

=n/2{2√2+n√2-√2}

=n/2{√2+n√2}

=n/2{√2(1+n)}

=√2.n.(n+1)/2