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# If y=1+x+(x^2/(2!))+(x^3/(3!))+(x^4/(4!))+..... oo so prove that ? (dy)/(dx) = y

## If y=1+x+(x^2/(2!))+(x^3/(3!))+(x^4/(4!))+..... oo so prove that $\frac{\mathrm{dy}}{\mathrm{dx}} = y$

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?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Jun 17, 2018

#### Explanation:

Here,

y=1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+...oo

(dy)/(dx)=0+1+(2x)/(2!)+(3x^2)/(3!)+(4x^3)/(4!)+(5x^4)/(5!)+...oo

(dy)/(dx)=1+(2x)/(2xx1!)+(3x^2)/(3xx2!)+(4x^3)/(4xx3!)+ (5x^4)/(5xx4!)+...oo

(dy)/(dx)=1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+...oo

$\frac{\mathrm{dy}}{\mathrm{dx}} = y$

Note :

(i)1! =1

(ii)2! =2xx1!

(iii)3! =3xx2!

(iv)4! =4xx3!
...............
................

n! =nxx(n-1)!

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