Binomial Expansion Formula

We are given that the 7th term in the expansion of is 700, and we are asked to determine the value of .

Step 1: The general term in the binomial expansion of is given by: We can rewrite the expression as: In this case, and . The general term will therefore be: We are interested in the 7th term, corresponding to (since the index starts from 0).

Step 2: Substitute into the formula for : Simplifying this gives: Since , we have:

Step 3: Simplify the expression for : We are told that , so we set the equation equal to 700: Simplifying this gives:

Step 4: Rearranging the terms gives a value for . Solving for yields . Thus, the value of is . \bigskip