 Hello and welcome to the session. Let us discuss the following question. It says using binomial theorem indicate which number is larger, 1.1 to the power 10000 or 1000. Now to solve this we will be using the expansion of A plus B whole to the power n and it is equal to nC0 A to the power n plus nC1 A to the power n minus 1B plus nC2 A to the power n minus 2B square so on and the last term will be nCn B to the power n. So this is the key idea behind this question. Let us now move on to the solution. Now 1.1 can be written as 1 plus 0.1 so 1.1 to the power 10000 can be written as 1 plus 0.1 whole to the power 10000. Now this is in the form A plus B whole to the power n where n is 10000, A is 1 and B is 0.1. Now we expand this using the expansion of A plus B whole to the power n. So 1 plus 0.1 whole to the power 10000 is equal to 10000 C0 1 to the power 10000 plus 10000 C1 1 to the power 10000 minus 1 that is 9999 into B that is 0.1. Now we will go on expanding this using the expansion of A plus B whole to the power n and we will see that we will have some positive terms. So plus other positive terms now this is equal to the first term is 1 because 10000 C0 is 1 and 1 to the power 10000 is 1 plus the second term is 10000 C1 is 10000 into 0.1 plus other positive terms. Now again this is equal to 1 plus 10000 into 0.1 is 1000 plus other positive terms. In this whole expression we see that we are adding some positive terms 2000 that means this whole term or the expression is strictly greater than 1000. Hence 1.1 to the power 10000 is strictly greater than 1000. So this completes the question. Hope you enjoyed this session. Goodbye and take care.