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Siliveru Anil Kumar
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#Educational Updates
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![Educational Updates - Sequences & Series special series Gsum formulas) Part 8 Specidl Series Some sfandard series have direct formulas to calculate the their quickly:| sums Sum of n natural numbers n(n + 1) Sum 1+ 2 + 3+ . + n ಕ 2 $ = 10<11 Example Find sum of first 10 numbers: 2 55 Sum of squares n(n + 1)(2n + 1) 12 + 22 + 32 + Sum + 3 n2 3x4x7 Example n = 3 S= 14 6 Sum of cubes n(n +1) Sum 13 + 23 + 33 + n3 ಕ + 2 (324)2 62 Example $ = 36 n = 3 = (1+2+3)2 13 + 23 + 33 (sum of natural numbers)2 Observation] Sum of cubes 3 Exam Trick Memorize 3 formulas: n(n+1) n(n+1)(2n+1) n(n+1) 2 2 mixing formulas Common mistakes wrong substitution calculation errors use correct formul Specidl series formulas save time in calculations: EduSphere Academy Page] 8 Sequences & Series special series Gsum formulas) Part 8 Specidl Series Some sfandard series have direct formulas to calculate the their quickly:| sums Sum of n natural numbers n(n + 1) Sum 1+ 2 + 3+ . + n ಕ 2 $ = 10<11 Example Find sum of first 10 numbers: 2 55 Sum of squares n(n + 1)(2n + 1) 12 + 22 + 32 + Sum + 3 n2 3x4x7 Example n = 3 S= 14 6 Sum of cubes n(n +1) Sum 13 + 23 + 33 + n3 ಕ + 2 (324)2 62 Example $ = 36 n = 3 = (1+2+3)2 13 + 23 + 33 (sum of natural numbers)2 Observation] Sum of cubes 3 Exam Trick Memorize 3 formulas: n(n+1) n(n+1)(2n+1) n(n+1) 2 2 mixing formulas Common mistakes wrong substitution calculation errors use correct formul Specidl series formulas save time in calculations: EduSphere Academy Page] 8 - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_857328_337f3826_1774466856049_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=049_sc.jpg "Educational Updates - Sequences & Series special series Gsum formulas) Part 8 Specidl Series Some sfandard series have direct formulas to calculate the their quickly:| sums Sum of n natural numbers n(n + 1) Sum 1+ 2 + 3+ . + n ಕ 2 $ = 10<11 Example Find sum of first 10 numbers: 2 55 Sum of squares n(n + 1)(2n + 1) 12 + 22 + 32 + Sum + 3 n2 3x4x7 Example n = 3 S= 14 6 Sum of cubes n(n +1) Sum 13 + 23 + 33 + n3 ಕ + 2 (324)2 62 Example $ = 36 n = 3 = (1+2+3)2 13 + 23 + 33 (sum of natural numbers)2 Observation] Sum of cubes 3 Exam Trick Memorize 3 formulas: n(n+1) n(n+1)(2n+1) n(n+1) 2 2 mixing formulas Common mistakes wrong substitution calculation errors use correct formul Specidl series formulas save time in calculations: EduSphere Academy Page] 8 Sequences & Series special series Gsum formulas) Part 8 Specidl Series Some sfandard series have direct formulas to calculate the their quickly:| sums Sum of n natural numbers n(n + 1) Sum 1+ 2 + 3+ . + n ಕ 2 $ = 10<11 Example Find sum of first 10 numbers: 2 55 Sum of squares n(n + 1)(2n + 1) 12 + 22 + 32 + Sum + 3 n2 3x4x7 Example n = 3 S= 14 6 Sum of cubes n(n +1) Sum 13 + 23 + 33 + n3 ಕ + 2 (324)2 62 Example $ = 36 n = 3 = (1+2+3)2 13 + 23 + 33 (sum of natural numbers)2 Observation] Sum of cubes 3 Exam Trick Memorize 3 formulas: n(n+1) n(n+1)(2n+1) n(n+1) 2 2 mixing formulas Common mistakes wrong substitution calculation errors use correct formul Specidl series formulas save time in calculations: EduSphere Academy Page] 8 - ShareChat")