Question

the value of 1/√2+1 + 1/√3+√2 + 1/√4+√3 + .............. + 1/√100+√99 is
(A) 1
(B) 9
(C) √99
(D) √99- 1​

Answer 1

Answer:

D

Step-by-step explanation:

..............,....

Answer 2

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(B) 9

Rationalise each term by multiplying them with their conjugate.

For example, (1/(√1+√2))*((√2–√1)/(√2–√1))

Which gives out √2 - √1

Second term -> √3 - √2

Third term -> √4 - √3

……………… & so on ....

Last term -> √100 - √99

Series: √2 - √1 + √3 - √2 + √4 - √3 .…..+ √99 - √98 + √100 -√99

Except (-√1) and (√100) , all the terms will cancel out.

So, -√1 + √100 = -1 + 10 = 9