Question

The value of 1+1/2+1/√2​

Answer 1

Step-by-step explanation:

rationalising each term,

1+

2

1

=

2

+1

1

×

2

−1

2

−1

=

2−1

2

−1

=

2

−1

2

+

3

1

=

3

+

2

1

×

3

−

2

3

−

2

=

3−2

3

−

2

=

3

−

2

............................

15

+4

1

=

4+

15

1

×

4−

15

4−

15

=

16−15

4−

15

=4−

15

∴ Given expression

=(

2

−1)+(

3

−

2

)+.....+4−

15

=4−1=3.

Answer 2

Answer:

$\frac{3+\sqrt{2} }{2}$

Step-by-step explanation:

$1+\frac{1}{2} +\frac{1}{\sqrt{2} }\\ =\frac{2\sqrt{2} }{2\sqrt{2} }+\frac{\sqrt{2} }{2\sqrt{2} }+\frac{2}{2\sqrt{2} }\\ =\frac{3\sqrt{2}+2 }{2\sqrt{2} }\\ =\frac{\sqrt{2} (3+\sqrt{2} )}{2\sqrt{2} }\\ =\frac{3+\sqrt{2} }{2}$