) Flashcards","topicId":"1ef0d7f9-62ab-4c35-9567-7ffef31c9af6","topicSlug":"sigma-notation","cards":[{"id":"ca07dca7-5eda-4cea-9515-5b41f33f9138","cardType":"basic","front":"Expand $\\displaystyle \\sum_{r=1}^{5}r^2$.","back":"$1^2+2^2+3^2+4^2+5^2$","points":1,"mcqOptions":null},{"id":"3d54505c-aff2-4ffe-8a40-d4c81b12890a","cardType":"cloze","front":"A finite sigma sum includes [ ].","back":"A finite sigma sum includes both the lower and upper limits.","points":null,"mcqOptions":null},{"id":"cc4fc417-c02c-426d-ba57-bf98c8d0bdc7","cardType":"cloze","front":"If the index runs from $a$ to $b$ inclusive, the number of terms is $\\text{[...]}$.","back":"If the index runs from $a$ to $b$ inclusive, the number of terms is $\\boxed{b-a+1}$.","points":null,"mcqOptions":null},{"id":"559cb6dc-9e9a-4e62-9df3-739dba9095b8","cardType":"basic","front":"Expand $\\displaystyle \\sum_{r=2}^{5}(r^2+1)$.","back":"$(2^2+1)+(3^2+1)+(4^2+1)+(5^2+1)$","points":1,"mcqOptions":null},{"id":"7ef2a0da-4843-4ff8-a1b2-35155ae98f04","cardType":"basic","front":"Evaluate $\\displaystyle \\sum_{r=2}^{6}(3r-1)$.","back":"$55$","points":2,"mcqOptions":null},{"id":"dd9aee58-4cba-46f5-a25d-ce0bd4d0dd27","cardType":"basic","front":"In $\\displaystyle \\sum_{r=1}^{n}r^2$, which quantity remains fixed throughout the summation?","back":"The upper limit $n$ remains fixed.","points":1,"mcqOptions":null},{"id":"d61046c3-16a3-4929-bbe3-01fdb5e61404","cardType":"basic","front":"Write $5+8+11+\\cdots+32$ in sigma notation, starting at $r=1$.","back":"$\\displaystyle \\sum_{r=1}^{10}(3r+2)$","points":2,"mcqOptions":null},{"id":"132aadfc-e97d-4dc1-aa7f-0237f2c3705a","cardType":"basic","front":"Write $4+7+10+\\cdots+40$ in sigma notation, starting at $r=1$.","back":"$\\displaystyle \\sum_{r=1}^{13}(3r+1)$","points":2,"mcqOptions":null},{"id":"3083239d-9c8d-4a25-b403-113aafc9297f","cardType":"basic","front":"What should substituting the lower limit into a proposed general term produce?","back":"It should produce the first term of the series.","points":1,"mcqOptions":null},{"id":"2b57a6c1-c331-449b-b329-0939c9e0dfbe","cardType":"basic","front":"What happens to a completed sum if its index letter is changed consistently?","back":"Its value is unchanged because the index is a placeholder.","points":1,"mcqOptions":null},{"id":"d688988a-5ac0-4edb-bbce-2f3d57ad8794","cardType":"cloze","front":"A constant summed from $r=a$ to $r=b$ satisfies $\\text{[...]}$.","back":"A constant summed from $r=a$ to $r=b$ satisfies $\\boxed{\\displaystyle \\sum_{r=a}^{b}c=c(b-a+1)}$.","points":null,"mcqOptions":null},{"id":"a5128ca7-a38d-4b91-b5b4-f4081278156f","cardType":"basic","front":"Evaluate $\\displaystyle \\sum_{k=3}^{8}7$.","back":"$42$","points":2,"mcqOptions":null},{"id":"9507d4e1-99cd-49aa-a2fe-4dc6f34821ea","cardType":"cloze","front":"Summation is linear over addition: $\\text{[...]}$.","back":"Summation is linear over addition: $\\boxed{\\displaystyle \\sum_{r=a}^{b}(u_r+v_r)=\\sum_{r=a}^{b}u_r+\\sum_{r=a}^{b}v_r}$.","points":null,"mcqOptions":null},{"id":"9a40ef25-5fd8-41f9-80fb-31ab93040efb","cardType":"cloze","front":"A constant factor can be extracted: $\\text{[...]}$.","back":"A constant factor can be extracted: $\\boxed{\\displaystyle \\sum_{r=a}^{b}cu_r=c\\sum_{r=a}^{b}u_r}$.","points":null,"mcqOptions":null},{"id":"4aa9e3df-db34-409a-b2dd-f9d2cf896dec","cardType":"basic","front":"Rewrite $\\displaystyle \\sum_{r=1}^{n}(3r^2-2r+5)$ using separate sums.","back":"$\\displaystyle 3\\sum_{r=1}^{n}r^2-2\\sum_{r=1}^{n}r+5n$","points":3,"mcqOptions":null},{"id":"c7ef4df3-b662-4255-adc4-7fd0b145aeb5","cardType":"basic","front":"Why can $r$ not

1.4.7 Sigma notation (A-level only) Flashcards

1.4.7 Sigma notation (A-level only) Flashcards