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  • The number of terms in the expansion of <img alt="(1+x)\left(1+x^{3}\right)\left(1+x^{6}\right)\left(1+x^{12}\right)\left(1+x^{24}\right) \ldots\left(1+x^{3

The number of terms in the expansion of (1+x)\left(1+x^{3}\right)\left(1+x^{6}\right)\left(1+x^{12}\right)\left(1+x^{24}\right) \ldots\left(1+x^{3 \times 2^{n}}\right) is 

Option: 1

2^{n+3}


Option: 2

2^{n+4}


Option: 3

2^{n+5}


Option: 4

None of these


Answers (1)

best_answer

After expansion, no two terms will have the same powers of x or the terms are non over- lapping. Therefore, the total number of terms =2 \times 2 \times 2 \times \ldots(n+2) times =2^{n+2} as a particular power of x can be chosen from each bracket in 2 ways.

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