Maharashtra State BoardHSC Science (General) 11th
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Answer the following: Find the coefficient of x6 in the expansion of e2x using series expansion - Mathematics and Statistics

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Sum

Answer the following:

Find the coefficient of x6 in the expansion of e2x using series expansion

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Solution

ex = `1 + x/(1!) + x^2/(2!) + x^3/(3!) + x^4/(4!) + x^5/(5!) + x^6/(6!) + ...`

∴ e2x = `1 + ((2x))/(1!) + (2x)^2/(2!) + (2x)^3/(3!) + (2x)^4/(4!) + (2x)^5/(5!) + (2x)^6/(6!)+ ...`

`=1 + 2/(1!)x + 2^2/(2!)x^2 + 2^3/(3!)x^3 + 2^4/(4!)x^4 + 2^5/(5!)x^5 + 2^6/(6!)x^6 + ...`

∴ coefficient of x6 = `2^6/(6!)`

= `(2 xx 2 xx 2 xx 2 xx 2 xx 2)/(6 xx 5 xx 4 xx 3 xx 2 xx 1)`

= `4/45`

Concept: Power Series
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Sequences and Series
Miscellaneous Exercise 2 | Q II. (32) | Page 42
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