Recall that Sf(n -f(n)+ f(n - 1)+ function of a real variable + f(1), where f is

Question

Recall that Sf(n -f(n)+ f(n - 1)+ function of a real variable + f(1), where f is an arbitrary Problem 1. Let c be a natural number. Prove that Inc+i + In +terms of lower degree in n c+1 using the methods of J. Bernoulli as presented on pp. 1-6 of the handout 9, Bernoulli on sums of powers. Other methods, including deducing this fact from the full Bernoulli formula, or using the ideas suggested at the end of the handout, will earn zero credit. Problem 2 (bonus). Let c be a natural number. Prove that nc+1nne + terms of lower degree in n c+1 12 using the methods of J. Bernouli as explained in Problem 1 you wil Hints for both problems. Do Problem 1 first. In order to do Problem 1 need to find the coefficient in front of nthe polvnomial (n 1)(n 2) (n-3). n -c) 12 3-4-. In order to do Proble m 2 you will need to find the coefficient in front of ne2

Explanation / Answer

Bernoulli's theorem states that energy of an incompressible and non-viscous fluid in steady flow through a pipe remains constant throughout the flow, provided there is no source or sink of the fluid along the length of the pipe.

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