Sigma Notation

Question 1

Which of the following is the correct expansion of $sum 5 2 2l ? l=1$

Not correct. Choice (a) is false.

Try again, you must multiply each term by 2.

Not correct. Choice (b) is false.

Try again, you must multiply each term by 2, not add 2.

Your answer is correct.

$5 sum 2l2 l=1$	=	$2× 12 + 2× 22 + 2× 32 + 2 × 42 + 2× 52$
	=	$2+ 8 + 18+ 32+ 50.$

Not correct. Choice (d) is false.

Try again, you need to multiply each term by 2 after you square it.

Question 2

Which of the following is the correct expansion of $sum 3 5k+1? k=1$

Not correct. Choice (a) is false.

Try again, the first term is incorrect.

Your answer is correct.

$3 sum 5k+1 = 51+1 + 52+1 + 53+1 = 52 + 53 + 54. k=1$

Not correct. Choice (c) is false.

Try again, you have calculated $sum 3 5k. k=1$

Not correct. Choice (d) is false.

Try again, you have omitted the last term.

Question 3

Which of the following correctly evaluates $sum n 5xj j=1$ where $x1 = 10, x2 = 14, x3 = - 2$ and $n = 3 ?$

Not correct. Choice (a) is false.

Try again, don’t forget the negative number.

Not correct. Choice (b) is false.

Try again, you have to multiply each number by 5.

Your answer is correct.

$sum 3 5xj = 5(x1 + x2 + x3) = 5(10+ 14 -2) = 5× 22 = 110 j=1$

Not correct. Choice (d) is false.

Try again, don’t forget the negative number and every term has to be multiplied by 5 .

Question 4

Which of the following is the correct expansion of $k sum +13(i- 2) -i+-2--? i=1$

Not correct. Choice (a) is false.

Try again, you last term is wrong

Not correct. Choice (b) is false.

Try again you have missed the first terms.

Not correct. Choice (c) is false.

Try again, you have missed the first few terms and the last term is wrong.

Your answer is correct.

$k sum +1 3(i--2)- i=1 i+ 2$	=	$3(1---2)+ 3(2--2) + 3(3---2)+ 3(4--2)+ ...+ 3(k+-1--2)- (1+ 2) (2 + 2) (3+ 2) (4 + 2) k + 1+ 2$
	=	$-3-+ 3 + 6+ 9 + ...+ 3(k---1). 3 5 6 7 k+ 3$

Question 5

Which one of the following statements is true?

Not correct. Choice (a) is false.

Try again - remember $sum 5 (ia + (i+ 1)b) = (a+ 2b)+ (2a+ 3b)+ (3a+ 4b)+ (4a + 5b)+ (5a + 6b). i=1$

Not correct. Choice (b) is false.

Try again, almost right.

Your answer is correct.

$5 sum (ia+ (i+ 1)b) i=1$	=	$(a + 2b)+ (2a + 3b) + (3a + 4b)+ (4a+ 5b)+ (5a+ 6b)$
	=	$(a + 2a+ 3a+ 4a + 5a)+ (2b + 3b + 4b+ 5b+ 6b)$
	=	$15a+ 20b.$

Not correct. Choice (d) is false.

Try again - remember $5 sum (ia + (i +1)b) = (a+ 2b)+ (2a+ 3b)+ (3a+ 4b)+ (4a+ 5b)+ (5a + 6b) i=1$
and we can only add like terms.


		Faculty of Economics and Business MathQuiz