Concept used: (a+b)(a−b)=a2−b2 Calculation: Consider the first term only, i.e.
1
1+√2
Rationalize the denominator ⇒
1
1+√2
×
√2−1
√2−1
⇒
√2−1
(√2)2−(1)2
⇒√2−1 After doing a similar operation in other terms, we will get √2−1+√3−√2+√4−√3......+√2021−√2020 ⇒√2021−1 ∴ Required value of the expression is √2021−1