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hello everyone Iamp;#39;m Norman wahlburger and welcome to algebraic calculus in this lecture weamp;#39;re going to pin down the sums of powers formulas letamp;#39;s go back to Feilhaber and also to Jacob Bernoulli so basically weamp;#39;re interested in this kind of series SK and N equals 1 to the k plus 2 to the k plus all the way up to n to the K in summation notation sum I equals 1 to N of I to the K and the exponents here the case are natural numbers 0 1 2 3 etc and weamp;#39;re interested in trying to establish or find a formula for these case powers running from 1 up to an arbitrary natural number n now we know so classically that there are these wonderful formulas for the case of K equals 1 2 amp;amp; 3 so the sum of the simply the natural numbers themselves from 1 up to n 1 plus 2 up to n is n times n plus 1 over 2 and the sum of the squares 1 squared plus 2 squared all the way up to N squared is this n times n plus 1 times 2n plus 1 over 6 while the sum of the c
