The following problems test your understanding of summation notation and binomial theorem. (a) Without using induction,...

 

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The following problems test your understanding of summation notation and binomial theorem. (a) Without using induction, prove that, for every positive integer n, TL km1 1 k(k+1) n n+1 4 Hint: Note that k(k+1) k+1* (b) Use (either version of the) Binomial Theorem to find the coefficients of 2¹7 and 18 in the polynomial (2r³-3r)7. (c) Without using induction, prove that, for every positive integer n, Σ'14 (3) οι 0. k=0 The following problems test your understanding of summation notation and binomial theorem. (a) Without using induction, prove that, for every positive integer n, TL km1 1 k(k+1) n n+1 4 Hint: Note that k(k+1) k+1* (b) Use (either version of the) Binomial Theorem to find the coefficients of 2¹7 and 18 in the polynomial (2r³-3r)7. (c) Without using induction, prove that, for every positive integer n, Σ'14 (3) οι 0. k=0