Can someone provide solutions and how to do it ? 3. What does the series 1+ 1/3
ID: 3887167 • Letter: C
Question
Can someone provide solutions and how to do it ?
3. What does the series 1+ 1/3 + 1/9+... F /) Pick Ex201(3converge to? the best answer. c) 3/2 d) 4/3 e) It diverges. a) Suppose your friend bakes six different kinds of donuts and asks you to choose three of them. How many ways are there for you to do this? The only thing that matters is the set of donuts chosen. 6. 3 120 b) Suppose you have a collection of 10 songs and want to play any three of them in some order, with no repetitions. How many ways can you do this, with different orders of the same songs counted as different? (0.9.2)(3-1) = 2166Explanation / Answer
3. 1+ 1/3+1/9+1/37+....
Sum of infinite geometric series converges to a1/(1-r) a1 is the first term and -1 <r < 1
r = a(n/)a(n-1) a(n) is the nth term a(n-1) is the n-1th term.
First term we know is 1/3
r = a2/a1 = (1/9)/(1/3)
r = 1/3
Replacing r in the expression for sum is (1/3)/(1-1/3) = 1/2
So S = 1/2
In that case out series 1+1/3+1/9.... will converge to 1 + 1/2 = 3/2
4. a)We need to select three donuts out of 6. So it is a classic case Combimation with 3 things to select out of 6 or 6C3 where n = 6 and r = 3
= nCr = n!/(n-r)!r! = 6!/3!*3! = 20
b) Classic case of arranging 3 items out of 10 items (Permutaion) . So nPr = n!/(n-r)! (With no repeatition)
10!/7! = 720