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Siliveru Anil Kumar
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#Educational Updates
#💼TSPSC/ APPSC ప్రత్యేకం
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![Educational Updates - Some Standard Formulae for Addition Sum of first 'n' natural numbers Usodin cilculalinn (olal' Mms in Ii"rodslruclurc, or pyromid stark +n = n(n +1) 1+2+3+ 2 Sum of first n even numbers 2+4+6+ +2n = n(n+1) planning infrapplledle with paired elements Sum of frst 'n' odd numbers (2n -1)=n2 1+3+5+ planfing and nd numbering systema Sum of the squares of first 'n' natural numbers n(n+1)(2n+1) 12 + 22 + 32 + + ಕ n? Calculares arem Suaua 6 for squara objecta II (olllrMrLon' Sum of square of first 'n' even numbers 22 + 42 + 62 + . + (2n)2 = 2n(n + ])(2n + ]) Used for structurall 3 engineoring calculutlons of evenly spated square elements Sum of square of first 'n' odd numbers] 1) n(4n2 12 + 32 + 55 + +(2n-1)2 = F {೦ಂಂ Essentlal for area 3 calculations in ~specialized artistic tiling Sum of cubes of first 'n' natural numbers] n(n + 1))2 + 33 + ٠٠٠٠٠ + n3 = 13 +23 Determines total volume 2 ol cublc itcms in storage' Sum of cubes of first 'n' even numbers (2n)3 23 2n2(n+1)2 +....+ +43 +66 ಕ Appll"dIn mal"ilnl Jllmnllon lor @ollstrucllon ' Sum of cubes of frst 'n' odd numbers 13 + 33+ 53+......+ (2n - 1)3 = n?(2n2 1) F Sum of cubes of first 'n' odd numbers Used in complex volume 13 + 33+ 53 +..+ (2n-1)3 = n2(2n2 calculations for unique 1) designs { Some Standard Formulae for Addition Sum of first 'n' natural numbers Usodin cilculalinn (olal' Mms in Ii"rodslruclurc, or pyromid stark +n = n(n +1) 1+2+3+ 2 Sum of first n even numbers 2+4+6+ +2n = n(n+1) planning infrapplledle with paired elements Sum of frst 'n' odd numbers (2n -1)=n2 1+3+5+ planfing and nd numbering systema Sum of the squares of first 'n' natural numbers n(n+1)(2n+1) 12 + 22 + 32 + + ಕ n? Calculares arem Suaua 6 for squara objecta II (olllrMrLon' Sum of square of first 'n' even numbers 22 + 42 + 62 + . + (2n)2 = 2n(n + ])(2n + ]) Used for structurall 3 engineoring calculutlons of evenly spated square elements Sum of square of first 'n' odd numbers] 1) n(4n2 12 + 32 + 55 + +(2n-1)2 = F {೦ಂಂ Essentlal for area 3 calculations in ~specialized artistic tiling Sum of cubes of first 'n' natural numbers] n(n + 1))2 + 33 + ٠٠٠٠٠ + n3 = 13 +23 Determines total volume 2 ol cublc itcms in storage' Sum of cubes of first 'n' even numbers (2n)3 23 2n2(n+1)2 +....+ +43 +66 ಕ Appll"dIn mal"ilnl Jllmnllon lor @ollstrucllon ' Sum of cubes of frst 'n' odd numbers 13 + 33+ 53+......+ (2n - 1)3 = n?(2n2 1) F Sum of cubes of first 'n' odd numbers Used in complex volume 13 + 33+ 53 +..+ (2n-1)3 = n2(2n2 calculations for unique 1) designs { - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_888540_1dd435c_1771777887038_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=038_sc.jpg "Educational Updates - Some Standard Formulae for Addition Sum of first 'n' natural numbers Usodin cilculalinn (olal' Mms in Ii\"rodslruclurc, or pyromid stark +n = n(n +1) 1+2+3+ 2 Sum of first n even numbers 2+4+6+ +2n = n(n+1) planning infrapplledle with paired elements Sum of frst 'n' odd numbers (2n -1)=n2 1+3+5+ planfing and nd numbering systema Sum of the squares of first 'n' natural numbers n(n+1)(2n+1) 12 + 22 + 32 + + ಕ n? Calculares arem Suaua 6 for squara objecta II (olllrMrLon' Sum of square of first 'n' even numbers 22 + 42 + 62 + . + (2n)2 = 2n(n + ])(2n + ]) Used for structurall 3 engineoring calculutlons of evenly spated square elements Sum of square of first 'n' odd numbers] 1) n(4n2 12 + 32 + 55 + +(2n-1)2 = F {೦ಂಂ Essentlal for area 3 calculations in ~specialized artistic tiling Sum of cubes of first 'n' natural numbers] n(n + 1))2 + 33 + ٠٠٠٠٠ + n3 = 13 +23 Determines total volume 2 ol cublc itcms in storage' Sum of cubes of first 'n' even numbers (2n)3 23 2n2(n+1)2 +....+ +43 +66 ಕ Appll\"dIn mal\"ilnl Jllmnllon lor @ollstrucllon ' Sum of cubes of frst 'n' odd numbers 13 + 33+ 53+......+ (2n - 1)3 = n?(2n2 1) F Sum of cubes of first 'n' odd numbers Used in complex volume 13 + 33+ 53 +..+ (2n-1)3 = n2(2n2 calculations for unique 1) designs { Some Standard Formulae for Addition Sum of first 'n' natural numbers Usodin cilculalinn (olal' Mms in Ii\"rodslruclurc, or pyromid stark +n = n(n +1) 1+2+3+ 2 Sum of first n even numbers 2+4+6+ +2n = n(n+1) planning infrapplledle with paired elements Sum of frst 'n' odd numbers (2n -1)=n2 1+3+5+ planfing and nd numbering systema Sum of the squares of first 'n' natural numbers n(n+1)(2n+1) 12 + 22 + 32 + + ಕ n? Calculares arem Suaua 6 for squara objecta II (olllrMrLon' Sum of square of first 'n' even numbers 22 + 42 + 62 + . + (2n)2 = 2n(n + ])(2n + ]) Used for structurall 3 engineoring calculutlons of evenly spated square elements Sum of square of first 'n' odd numbers] 1) n(4n2 12 + 32 + 55 + +(2n-1)2 = F {೦ಂಂ Essentlal for area 3 calculations in ~specialized artistic tiling Sum of cubes of first 'n' natural numbers] n(n + 1))2 + 33 + ٠٠٠٠٠ + n3 = 13 +23 Determines total volume 2 ol cublc itcms in storage' Sum of cubes of first 'n' even numbers (2n)3 23 2n2(n+1)2 +....+ +43 +66 ಕ Appll\"dIn mal\"ilnl Jllmnllon lor @ollstrucllon ' Sum of cubes of frst 'n' odd numbers 13 + 33+ 53+......+ (2n - 1)3 = n?(2n2 1) F Sum of cubes of first 'n' odd numbers Used in complex volume 13 + 33+ 53 +..+ (2n-1)3 = n2(2n2 calculations for unique 1) designs { - ShareChat")