Use the principle of mathematical induction to show that the given statement is true for all natural numbers 11 + 23 +35+ +(12n-1)=n(6n+5) 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) how does this result demonstrate that 11 +23+35++(12n-1)=n(6n + 5) is true for all natural numbers n? o a. since the expressions on the left and right sides of the statement fork+1 are equivalent when 1 and when k2, the given statement is true for all natural numbers n. o b. the statement holds for k+1, given that it holds for k. now show that the statement is true fork +2. given that it is true fork+1 ос. since the expressions on the left and right sides of the statement fork+ 1 are equivalent, the statement holds fork+1, given that it holds fork. this is the second condition that must be satisfied for the given statement to be true for all natural numbers n. o d. since the expressions on the left and right sides of the statement fork+ 1 are not equivalent, the statement does not hold fork+ 1 given that it holds for however, since the given statement is true for n= 1, it is true for all natural numbers n. click to select your answer(s) copyright © 2019 pearson education inc. all rights reserved. terms of use privacy policy. permissions e a te