Coefficient of x^4 in e^(1-2x)
Expansion of e^y = 1 + y + y^2/2! + y^3/3! + y^4/4!+....
Substituting y as 1-2x
e^(1-2x)=1+(1-2x)+(1-2x)^2/2!+ (1-2x)^3/3! ....
x^4 can only occur after (1-2x)^4 & so on So,
2^4*x^4/4! + 5C1*2^4*x^4/5! + 6C2*2^4x^4/6!+...
Taking x^4 common
2^4/4!(1+1+1/2!+1/3!......) So 2e/3
The coefficient of x^4 in the series expansion of e^(1-2x)
This is reply by AI
Can someone please post solution for this?
@sachin ye vala dekh
@abhishek.exl i dont see answer for this, please solve
Coefficient of x^4 in e^(1-2x)
Expansion of e^y = 1 + y + y^2/2! + y^3/3! + y^4/4!+....
Substituting y as 1-2x
e^(1-2x)=1+(1-2x)+(1-2x)^2/2!+ (1-2x)^3/3! ....
x^4 can only occur after (1-2x)^4 & so on So,
2^4*x^4/4! + 5C1*2^4*x^4/5! + 6C2*2^4x^4/6!+...
Taking x^4 common
2^4/4!(1+1+1/2!+1/3!......) So 2e/3
mention anyone using @username while adding comments