Prove that (from i=1 to n) sum([1/((2i-1)(2i+1))] = n/(2n+1). if true use induction, else give smallest value of n that it is false for.

The statement is true

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,

We will prove our base case, when n=1, to be true.

base case:

Inductive hypothesis:

Now, we will assume the induction hypothesis and then uses this assumption, involving n, to prove the statement for n + 1.

Inductive step:

With this we have proved our statement to be true for n+1.

In conlusion, for every natural .

answer: options

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: