Question

√5+√5+√5+..........?​

Answer 1

let the total terms be,

"n"

Using sum to 'n' terms of A.P

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

d=0

n/2x2a

=>an

therefore,

Sn=an

and.

a=√5

so,

sn=n√5

thanks!

Answer 2

$\frac{2 \: + \: \sqrt{5} \: + \: \sqrt{16 \: - \: 6 \sqrt{5} } }{2} = 2.7472$

This is a theorem found in Ramanujams Notebook 4.

It is toooo difficult to prove.