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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\r

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) \text { 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 × 2 × 2 ×  . . . (n +2) times = 2n+2 as a particular power of x can be chosen  from  each bracket  in  2 ways.

 

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Rishi

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