Question

find this one ...... Mathematics​

Answer 1

Heya,

i) 1/ ( √2 + √ 1 )

= ( √ 2 - √ 1 )/[( √ 2 + √ 1 )( √ 2 - √ 1 )]

= ( √ 2 - √ 1 )/[ ( √ 2 )^2 - ( √ 1 )^2]

= ( √ 2 - √ 1 )/ ( 2 - 1 )

= √ 2 - √ 1

Similarly,

ii ) 1/ ( √ 2 + √ 3 ) = √ 3 - √ 2

Now,

1/ ( √ 2 + √ 1 ) + 1/ ( √ 2 + √ 3 ) +........+1/ ( √ 8 + √ 9 )

= √ 2 - √ 1 + √ 3 - √ 2 + √ 4 - √ 3 +....+ √ 9 - √ 8

= - √ 1 + √ 9

= - 1 + 3

= 2