 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says find an approximation of 0.99 raised to the power 5 using the first three terms of its expansion. Here is what begin with the solution and we have to find the approximation of 0.99 raised to the power 5 which can further be written as 1 0.01 raised to the power 5. Now we are using binomial expansion on expanding it can further be written as 5C0 1 raised to the power 5 into minus 0.01 raised to the power 0 plus 5C1 1 raised to the power 4 into minus 0.01 raised to the power 1 plus 5C2 1 raised to the power 3 into minus 0.01 raised to the power 2 plus so on this is further equal to 5C0 is 1 1 raised to the power 5 is again 1 and minus 0.01 raised to the power 0 is 1 plus 5C1 is 5 1 raised to the power 4 is 1 into minus 0.01 raised to the power 1 is 0.01 with a negative sign plus 5C2 is 10 1 raised to the power 3 is 1 and minus 0.01 raised to the power 2 is equal to plus 0.0001 so on this is further equal to 1 minus 0.05 plus 0.001 plus so on now since we have to find the approximation using the first three terms so these are the first three terms therefore this further equal to now adding the first and third term we have 1.001 minus 0.05 which is further equal to also practicing 0.05 from 1.001 we have 0.9510 thus on approximating 0.99 raised to the power 5 our answer is 0.9510 so this completes the session take care and have a good day