Thread: Problem related to sequence and series

Q- Find the sum of the series?

1/(2^1/2 + 1^1/2) + 1/(2^1/2 + 3^1/2) + ......... + 1/(120^1/2 + 121^1/2)

Any help would be greatly appreciated.

Thanks,
Ashish

Write
1 = sqrt(2)^2 - sqrt(1)^2

1 = sqrt(3)^2 - sqrt(2)^2

1 = sqrt(4)^2 - sqrt(3)^2

.
.
.
.

Remember that

sqrt(a)^2 - sqrt(b)^2 ={sqrt(a) - sqrt(b)} x {sqrt(a) + sqrt(b)}


Use this formula for each term many things will be cancelled .. ..

Originally Posted by a69356

Q- Find the sum of the series?

1/(2^1/2 + 1^1/2) + 1/(2^1/2 + 3^1/2) + ......... + 1/(120^1/2 + 121^1/2)

Any help would be greatly appreciated.

Thanks,
Ashish

Note that .

You series is then

Write out several terms to see what is going to happen.