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Find the nd term in the expansion of in simplest form.Answer:
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Q. Find the nd term in the expansion of in simplest form.Answer:
- Use Binomial Theorem: To find the nd term in the expansion of , we will use the binomial theorem. The general form of the -th term in the expansion of is given by , where is the binomial coefficient. For the nd term, .
- Calculate Binomial Coefficient: First, we calculate the binomial coefficient for the nd term, which is (since ). is the number of combinations of items taken at a time, which is simply .
- Raise First Term to Power: Next, we raise the first term of the binomial, , to the power of which is . So, .
- Raise Second Term to Power: Then, we raise the second term of the binomial, , to the power of which is . So, .
- Multiply Coefficient and Terms: Now, we multiply the binomial coefficient by the powers of the first and second terms. The nd term of the expansion is .
- Simplify the Expression: Finally, we simplify the expression to get the nd term in its simplest form. The nd term is .
