Use the principle of mathematical induction to show that the given statement is true for all natural numbers n. 11 +23 +35+ +(12n-1)=n(6n+5) write the given statement fork+1. 11 +23+35+ . . +(12k-1)+= now, according to the principle of mathematical induction, assume that 11 +23 +35++(12k-1) use this assumption to rewrite the left side of the statement for k+1. what is the resulting expression? simplifying this expression and factoring gives (k+ 1)(ii how does this result demonstrate that 11 +23+35+ . . +(12n-1)=n(n+ 5) is true for all natural numbers n? - 2. the given st o a. since the expressions on the left and right sides of the statement for k+1 are equivalent when k = 1 and when natural numbers n click to select your answer(s). copyright © 2019 pearson education inc. all rights reserved. terms of use privacy

(01.03 mc) which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4. select one: a. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1. b. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12. c. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3. d. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.