vel only) Flashcards","topicId":"3accba51-1403-41b7-8535-6032969eaa1b","topicSlug":"sigma-notation","cards":[{"id":"d4a7619d-dd5f-4214-bb69-3f07059b48ce","cardType":"cloze","front":"In $\\sum_{r=1}^{5}(2r+1)$, $r$ is the [ ].","back":"In $\\sum_{r=1}^{5}(2r+1)$, $r$ is the index of summation.","points":null,"mcqOptions":null},{"id":"aff2de12-fefb-4cad-bbb8-49f0108a8c5e","cardType":"cloze","front":"The limits in a sigma sum are [ ].","back":"The limits in a sigma sum are inclusive.","points":null,"mcqOptions":null},{"id":"382341b9-92ad-45a3-b121-b8b479a15d6c","cardType":"basic","front":"How many terms are in $\\sum_{r=a}^{b}f(r)$?","back":"$b-a+1$ terms.","points":1,"mcqOptions":null},{"id":"c19e03ab-7b1a-4b05-94ab-cf5860135f79","cardType":"basic","front":"Which index values are used in $\\sum_{k=3}^{6}(k^2-1)$?","back":"$k=3,4,5,6$.","points":1,"mcqOptions":null},{"id":"5dbf1d77-f9f0-434e-94f8-d991403ca715","cardType":"basic","front":"Expand $\\sum_{r=1}^{5}(2r+1)$ into simplified terms.","back":"$3+5+7+9+11$.","points":1,"mcqOptions":null},{"id":"2291ccd9-1759-4ec9-839a-e9e9b9652bad","cardType":"basic","front":"Evaluate $\\sum_{r=1}^{5}(2r+1)$.","back":"$35$.","points":1,"mcqOptions":null},{"id":"a5aad545-fdbb-4620-b271-beb1cfd1be4d","cardType":"basic","front":"Evaluate $\\sum_{k=3}^{6}(k^2-1)$.","back":"$82$.","points":1,"mcqOptions":null},{"id":"ef407b95-aeac-44dd-9027-cecb776016be","cardType":"basic","front":"What happens to $\\sum_{r=1}^{5}r^2$ if every $r$ is consistently replaced by $k$?","back":"The sum is unchanged.","points":1,"mcqOptions":null},{"id":"e5652292-435a-443c-bc10-c406cc4058fc","cardType":"basic","front":"Why should an index not be renamed using a letter already present elsewhere in the expression?","back":"The letter already has another meaning.","points":2,"mcqOptions":null},{"id":"d4c59203-fc2a-4945-8b5b-9c9c2bf4102d","cardType":"cloze","front":"A constant factor can be taken outside a sum: $\\sum_{r=a}^{b}c f(r)=$ $\\text{[...]}$.","back":"A constant factor can be taken outside a sum: $\\sum_{r=a}^{b}c f(r)=$ $\\boxed{c\\sum_{r=a}^{b}f(r)}$.","points":null,"mcqOptions":null},{"id":"3aa26246-f44d-4b88-bb4f-d172c8371273","cardType":"basic","front":"Rewrite $\\sum_{r=a}^{b}(f(r)-g(r))$ as separate sums.","back":"$\\sum_{r=a}^{b}f(r)-\\sum_{r=a}^{b}g(r)$.","points":1,"mcqOptions":null},{"id":"1110bf2e-b823-4a63-88b2-4baf449412e0","cardType":"basic","front":"Evaluate $\\sum_{r=a}^{b}c$.","back":"$c(b-a+1)$.","points":1,"mcqOptions":null},{"id":"e226e7d0-18c9-43a5-a4b1-3bf164f198f7","cardType":"basic","front":"Why can an added constant not simply be taken outside $\\sum$?","back":"It is added once for every index value.","points":2,"mcqOptions":null},{"id":"45a96656-b40a-47b7-8151-436ddff39a2e","cardType":"cloze","front":"For positive integer $n$, $\\sum_{r=1}^{n}r=$ $\\text{[...]}$.","back":"For positive integer $n$, $\\sum_{r=1}^{n}r=$ $\\boxed{\\frac{n(n+1)}{2}}$.","points":null,"mcqOptions":null},{"id":"40fd8f73-ce6b-4323-97aa-08a36ec13a63","cardType":"cloze","front":"For positive integer $n$, $\\sum_{r=1}^{n}r^2=$ $\\text{[...]}$.","back":"For positive integer $n$, $\\sum_{r=1}^{n}r^2=$ $\\boxed{\\frac{n(n+1)(2n+1)}{6}}$.","points":null,"mcqOptions":null},{"id":"c43745ae-b21b-45f2-ab42-e7eda2e2e992","cardType":"cloze","front":"For positive integer $n$, $\\sum_{r=1}^{n}1=$ $\\text{[...]}$.","back":"For positive integer $n$, $\\sum_{r=1}^{n}1=$ $\\boxed{n}$.","points":null,"mcqOptions":null},{"id":"c0b9f4df-469a-419e-91da-b9c3a05c941b","cardType":"basic","front":"Write $7+10+13+\\cdots+40$ using sigma notation with index starting at 1.","back":"$\\sum_{r=1}^{12}(3r+4)$.","points":2,"mcqOptions":null

1.6.9 Sigma notation (A-level only) Flashcards

1.6.9 Sigma notation (A-level only) Flashcards