Question

plz answer this with proper explanation

Answer 1

Given, x = √[ 1 + √1 + √1 .......... (1)

here , √[ 1 + √1 + √1 ............is an infinite series .

and we know that when the series is infinite series.

then , according to the property of infinite series:

√[p+√p +√p .....=[√(4p+1) + 1 ] / 2


so now , we have ,


x=√ [1 + √1 + √1 ...........

here , p = 1

x = [√{4(1) + 1)}+ 1 ]/ 2



x = (√5 + 1 )/ 2




therefore,


the value of x = (√5 + 1 )/ 2


--------------------------------------------------------

second important property :

when the series is finite ( means not infinite )

then, √( p + √p + √p )

= p^[ (2^n - 1) ÷ 2^n ]

where,

n is the number of times p repeated.

--------------------------------------------------------