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the coefficient of x^n in the expansion (1+x/1!+x^2/2!+x^3/3!..........)^2 is

the coefficient of x^n in the expansion (1+x/1!+x^2/2!+x^3/3!..........)^2 is

Grade:11

2 Answers

Master Ani
35 Points
6 years ago
Clearly this is (ex)2
which can be written as e2x by law of exponents
 
replacing x with 2x in infinite series of e^x
 
1+(2x/1!) + ((2x)2 /2!) + ((2x)3 /3!) + ….
 
we get the coefficient of n’th term of this expansion as ((2x)n)/n! which can also be written as 2nxn/n! 
 
ankit singh
askIITians Faculty 614 Points
3 years ago
learly this is (ex)2
which can be written as e2x by law of exponents
 
replacing x with 2x in infinite series of e^x
 
1+(2x/1!) + ((2x)2 /2!) + ((2x)3 /3!) + ….
 
we get the coefficient of n’th term of this expansion as ((2x)n)/n! which can also be written as 2nxn/n!

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