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Sigma Notation - Quiz 2   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which one of the following is the correct expansion of  sum 6 2i? i=1
a) sum 6 2i = 2+ 4+ 6. i=1   b) 6 sum 2i = 2 + 4+ 6+ 8+ .... i=1
c) sum 6 2i = 2+ 4+ 8 + 16+ 32+ 64. i=1   d) sum 6 2i = 2+ 4+ 6 + 8+ 10+ 12. i=1

 

Not correct. Choice (a) is false.
Try again, you must have 6 terms.
Not correct. Choice (b) is false.
Try again, you must stop after 6 terms.
Not correct. Choice (c) is false.
Try again, you have expanded  sum 6 i 2. i=1
Your answer is correct.
6 sum 2i = 2 × 1+ 2× 2 + 2× 3+ ...+ 2× 6 = 2 + 4+ 6+ 8 + 10+ 12. i=1
Question 2 lion

Which one of the following is the correct expansion of  sum 7 3j- 1? j=3
a) sum 7 j-1 3 4 5 6 7 3 = 3 + 3 + 3 + 3 + 3 . j=3   b) 7 sum 3j-1 = 33 + 34 + 35 + 36. j=3
c) sum 7 3j-1 = 32 + 33 +34 + 35 + 36 + 37. j=3   d) sum 7 3j-1 = 32 + 33 + 34 + 35 + 36. j=3

 

Not correct. Choice (a) is false.
Try again, you have found sum 7 j 3 j=3
Not correct. Choice (b) is false.
Try again, you haven’t started at the correct term.
Not correct. Choice (c) is false.
Try again, you haven’t finished at the correct term.
Your answer is correct.
sum 7 j-1 3- 1 4- 1 5- 1 6-1 7-1 2 3 4 5 6 3 = 3 + 3 + 3 + 3 + 3 = 3 + 3 +3 + 3 + 3 . j=3
Question 3 lion

The sum  5 1 sum x 5 k=1 k   is equal to which of the following?
a) 5 1 sum x = x1 + x2 + x3+ x4+ x5 . 5 k=1 k 5 5 5 5 5   b) sum 5 1 xk = x1+ x2+ x3 + x4 + x5. 5 k=1 1 2 3 4 5
c) 1 sum 5 1 5 xk = 5x1 + x2 + x3 + x4 + x5 . k=1   d) 1 sum 5 1 - xk = -(x1 + x2 +x3 + ...) . 5 k=1 5

 

Your answer is correct.
Not correct. Choice (b) is false.
Try again. The only number that changes is the subscript of the xk.
Not correct. Choice (c) is false.
Try again, each term is multiplied by 1 -. 5
Not correct. Choice (d) is false.
Try again, there are only 5 terms in this sum.
Question 4 lion

Which of the following is the correct expansion of  m sum t- 1 2 ----? t=2 t+ 1
a) m 2 sum t--1= 2+ 4 + 6 + ...+ 2(m---1). t=2 t+ 1 3 4 5 m + 1   b) sum m 2 t--1 = 2 + 3 + 4+ ...+ (m---1). t=2t +1 3 4 5 m + 1
c) m sum t--1 3 5 7 2m---1 2 t+ 1 = 3 + 4 + 5 + ...+ m + 1 . t=2   d) sum m 2 t--1= 2+ 2 + 3 + ...+ m---1 . t=2 t+ 1 3 4 5 m +1

 

Your answer is correct.
m sum t- 1 2 t+-1 t=2 = ((2- 1) (3- 1) (4- 1) m - 1 ) 2 × -2+-1- + -3+-1-+ -4+-1- + ...+ m-+-1
 =2+ 4 + 6 + ...+ 2(m---1). 3 4 5 m + 1
Not correct. Choice (b) is false.
Try again, you have not calculated the numerators correctly.
Not correct. Choice (c) is false.
Try again, you have found sum m (2t--1). t=2 t +1
Not correct. Choice (d) is false.
Try again, you only multiplied the first term by 2, not every term.
Question 5 lion

Which of the following is the expansion of sum n -1--- (xi- x)2 n- 1 i=1 where n = 5.
a) ( ) (x1--x)+-(x2--x)+-(x3--x)+-(x4--x)-+-(x5---x) 2 5
b) (x1- x)2 + (x2- x)2 + (x3- x)2 + (x4- x)2 + (x5- x)2 -----------------------4------------------------
c) (x1--x)2 +-(x2--x)2 +-(x3--x)2 +-(x4--x)2 +-(x5--x)2 5
d) (x1--x)2 (x2--x)2 (x3--x)2 (x4--x)2 (x5---x)2 1 + 2 + 3 + 4 + 5

 

Not correct. Choice (a) is false.
Try again, you have made several mistakes.
Your answer is correct.
1 sum n ----- (xi- x)2 n - 1 i=1 =1 sum 5 - (xi- x)2 4 i=1
 = ( ) 1 (x1 - x)2 + (x2 - x)2 + (x3 - x)2 + (x4 - x)2 + (x5 - x)2 4
 =(x - x)2 + (x - x)2 + (x - x)2 + (x - x)2 + (x - x)2 --1---------2---------3-4-------4---------5----- .
Not correct. Choice (c) is false.
Try again, you have the wrong denominator.
Not correct. Choice (d) is false.
Try again, the denominator should be fixed.