 Hello and welcome to the session. In this session we discuss the following question which says evaluate the limit limit n tends to infinity 1 upon 2 plus 1 plus 3 upon 2 plus unfair on plus n upon 2 this way upon n square upon 4 plus n plus 3. Let's now move on to the solution. We are supposed to find the limit limit n tends to infinity 1 upon 2 plus 1 plus 3 upon 2 plus n sir n plus n upon 2 and this will upon n square upon 4 plus n plus 3. We are given as limit n tends to infinity. Now taking 1 upon 2 common from the numerator we get 1 upon 2 into 1 plus plus 3 plus and so on we hold and this will upon 4 common from the denominator we get 1 upon square into n square plus and this is equal to limit n tends to infinity 1 upon 2 into now 1 plus 2 plus 3 plus and so on plus n minus this sum is equal to n into n plus 1 the whole upon 2 and we can write n into n plus 1 the whole and this will upon 2 and this will upon 1 upon 4 into n square plus 2 the whole. Suppose that we have limit n tends to infinity 1 upon 4 into n plus 1 the whole would be plus n the whole and this will upon 1 upon 4 into n square plus 1 the whole. This 1 upon 4 1 upon 4 times this and so this is equal to limit n tends to infinity 2 upon n square plus 4n dividing action which is n square so the value in the numerator and denominator by n square limit infinity 1 plus 1 upon n this will upon 1 plus 12 upon n square n to 0 upon n square with n to 0 therefore this limit would be equal to 1 plus 0 since 1 upon n would be 0 this upon 1 plus 0 so this is equal to 1 quiet limit which is infinity 1 upon 2 plus 1 is equal to 1 but we have understood the solution of this question.