查看完整版本 : M2 Differentiation

E.H 2015-8-16 05:10 PM

M2 Differentiation

Q98
It's given that
1+x+x^2+...+x^(n-1)=(x^-1)÷(x-1)......(*)
where x not equal to 1 and n is a positive integer
a)by differentiation bith sides of(*)with respect to x,prove that
1+2x+3x^2+...+(n-1)x^(n-2)=[(n-1)x^-nx^(n-1)+1]÷(x-1)^2
b)using the result of a,find the value of 1+2(3)+3(3)^2+...+13(3)^12
thanks



[url=http://www.discuss.com.hk/android][img=100,23]http://i.discuss.com.hk/d/images/r10/androidD.jpg[/img][/url]

kiwakwok 2015-8-16 08:12 PM

First the correct formula for (*) should be
1+x+x^2+...+x^(n-1)=(x^n-1)÷(x-1)

By differentiation of both sides of (*), we have
0 + 1 + 2x + 3x^2 + ... + (n-1)x^(n-2)=[(x-1)(nx^(n-1)) - (x^n-1)]/(x-1)^2=[(n-1)x^n - nx^(n-1) + 1]/(x-1)^2

Take x = 3 and n = 14, and then find the answer.

E.H 2015-8-17 01:01 AM

Oops U're right.I typed it incorrect
Thanks������



[url=http://www.discuss.com.hk/android][img=100,23]http://i.discuss.com.hk/d/images/r10/androidD.jpg[/img][/url]
頁: [1]
查看完整版本: M2 Differentiation