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Aaradhya Ranjan

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--- - SUM OF SOME IMPORTANT SERIES Sum of frst n(n+1) narural numbers 1+2+3+ . +11 = Sum of first n even 2+4+6+...+2n="("+1) natural numbers Sum of frsf n odd 1+3+5+...+(2n-1)=n narural numbers ("+1)-(2n+1) Sum of squares of 7 12+ 22 + 32+ .. +7 ` frst n natural numbers Zn-("+1)-(2"+1) Sum of squares of (2n)2 22+42+6+ .+ frst n even narural numbers n : (4n7 Sum of squqres of -(2n -1)3= 12+ 32+5+ .. + frst n natural odd numbers Sum of cubes of + . +"'= " (n+1" first n natural 1+ 23+ 31 numbers Sumn or cubes or hrs1' 2' + 4 + 6 + : +(2) = 2೫? . (" + I)? even nurural numoers; Sum of cubes of 13+33+5+.. +(2n-1) '= n? . (2n2_1) first odd nqfurql numbers SUM OF SOME IMPORTANT SERIES Sum of frst n(n+1) narural numbers 1+2+3+ . +11 = Sum of first n even 2+4+6+...+2n="("+1) natural numbers Sum of frsf n odd 1+3+5+...+(2n-1)=n narural numbers ("+1)-(2n+1) Sum of squares of 7 12+ 22 + 32+ .. +7 ` frst n natural numbers Zn-("+1)-(2"+1) Sum of squares of (2n)2 22+42+6+ .+ frst n even narural numbers n : (4n7 Sum of squqres of -(2n -1)3= 12+ 32+5+ .. + frst n natural odd numbers Sum of cubes of + . +"'= " (n+1" first n natural 1+ 23+ 31 numbers Sumn or cubes or hrs1' 2' + 4 + 6 + : +(2) = 2೫? . (" + I)? even nurural numoers; Sum of cubes of 13+33+5+.. +(2n-1) '= n? . (2n2_1) first odd nqfurql numbers - ShareChat

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