Number-Theory
Question 1 |
What is the sum to infinity of the series,
3 + 6x2 + 9x4 + 12x6 +.... given |x|<1?
3 + 6x2 + 9x4 + 12x6 +.... given |x|<1?
3/(1+x2) | |
3/(1+x2)2 | |
3/(1-x2)2 | |
3/(1-x2) |
Question 1 Explanation:
s(n)=3+6x2 + 9x4 + 12x6 +....
-x2 s(n)=-3x2 - 6x4 - 9x6 -12x4....
(1-x2)s(n)=3+3x2+3x4+3x6......
=3(1+x2 + x4 + x6 +....)
(1-x2)s(n)=3*(1/(1-x2)
a=1, r=x i.e<1
s(n)=3/(1-x2)2
-x2 s(n)=-3x2 - 6x4 - 9x6 -12x4....
(1-x2)s(n)=3+3x2+3x4+3x6......
=3(1+x2 + x4 + x6 +....)
(1-x2)s(n)=3*(1/(1-x2)
a=1, r=x i.e<1
s(n)=3/(1-x2)2
Question 2 |
Find the average of the squares of the consecutive odd numbers from 1 to 21
162 | |
161 | |
159 | |
160 |
There are 2 questions to complete.