Let S = N ∪ { 0 } . Define a relation R from S to R by : R = { ( x , y ) : lo g e y = x lo g e ( 5 2 ) , x ∈ S , y ∈ R } Then, the sum of all the elements in the range of R is equal to :

Question

Let S = N ∪ { 0 } . Define a relation R from S to R by : R = { ( x , y ) : lo g e ​ y = x lo g e ​ ( 5 2 ​ ) , x ∈ S , y ∈ R } Then, the sum of all the elements in the range of R is equal to :

TestHub · Accepted Answer

​ S = { 0 , 1 , 2 , 3 …… } lo g y ​ y = lo g e ​ ( 5 2 ​ ) ⇒ y = ( 5 2 ​ ) x ​ Required Sum = 1 + ( 5 2 ​ ) 1 + ( 5 2 ​ ) 2 + ( 5 2 ​ ) 3 + … .. − = 1 − 5 2 ​ 1 ​ = 3 5 ​

Mathematics - SET AND RELATION Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main (2026)