Prove the following using the definition of convergence for sequences: (a) lim 0, where pe R,...

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Prove the following using the definition of convergence for sequences: (a) lim 0, where pe R, p > 0. 1 n-∞ np (b) lim n-x (c) lim n-x = n 2 = 0. 1+2+3+ +n 1 2 = 0. (Hint: Multiply and divide by the conjugate first.) ... n² (d) lim (√n+1-√n) nx Prove the following using the definition of convergence for sequences: (a) lim 0, where pe R, p > 0. 1 n-∞ np (b) lim n-x (c) lim n-x = n 2 = 0. 1+2+3+ +n 1 2 = 0. (Hint: Multiply and divide by the conjugate first.) ... n² (d) lim (√n+1-√n) nx