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Asked by universitymails6 | 22 Jun, 2022, 07:15: PM

Expert Answer

Q: If the sum of the coefficients in the expansion of (a+b)ⁿ is 4096, then the greatest coefficient in the expansion is

Solution:

The space greatest space coefficient space is colon space to the power of straight n straight C subscript straight n over 2 end subscript space when space straight n space is space even to the power of straight n straight C subscript fraction numerator straight n plus 1 over denominator 2 end fraction end subscript space and space to the power of straight n straight C subscript fraction numerator straight n minus 1 over denominator 2 end fraction end subscript Sum space of space the space coefficients space of space left parenthesis straight a plus straight b right parenthesis to the power of straight n equals 2 to the power of straight n space Therefore comma space 2 to the power of straight n equals 4096 equals 2 to the power of 12 rightwards double arrow straight n equals 12 comma space which space is space even So comma space the space greatest space coefficient space equals to the power of 12 straight C subscript 6 equals 924

Answered by Renu Varma | 25 Jun, 2022, 12:34: PM

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