Use mathematical induction prove that: ¼+2*¼+4*¼+....+[2(n-1)+¼]=4n²-3n/4 these are sooo confusing

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Use mathematical induction prove that: ¼+2*¼+4*¼+....+[2(n-1)+¼]=4n²-3n/4 these are sooo confusing

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

you've got to take steps: 1) Show that P(1) is true 2) Assume P(k) is true 3) find P(k+1) ^_^
now to show that p(1) is true : P(1) : 2(1-1) = 4(1)^2-3(1)/4<-- are you sure of the equation?
theres a 1/4 lol

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

oh right >_< thank you :)
so after that, you do the calculation and if it's true proceed to step (2)
its the same as the other induction question you put essentually
expect this time it wont be so easy to simplify the expression in step 3
2) Assume p(k) :<-- in this case, replace the n's with k ^_^
except
are you getting the picture 2BGood? :)
i know it's like the other one, and you explained the other one so well, but i look at the problem and go????????????
ksajflkdaf
yep ^_^ , just following the steps dear
lol Mak :)
follow*
Assume S(k)= ( 4k^2 -3k) / 4 We need to prove that S(k+1) = [4(k+1)^2 -3(k+1) ] / 4
alright, elec got it from here, good luck :)
remember that I got the second line above by sub n=k+1 into the expression on the RHS of the sum
Now, we also know the result S(k+1) = S(k) +T(k+1) , very important result you need to know to summation induction questions
all you've got to do is plug in k+1 in the sequence then prove that the LHS and RHS are equal. LHS= .... (simplify it) then check if you get the same thing with the RHS >_< LOL
so we know that S(k+1) =[ [ 4k^2 -3k ] / 4] +( 2k + (1/4) )
the first fraction comes from the assumption , the second bracket comes from subbing n=k+1 into the general term on the LHS , thats our (k+1)th term
now its just a matter of algebra
S(k+1) =[ 4k^2 -3k +8k +1 ] / 4 by getting over a common denominator
2BGood, are you getting the picture? ^_^
now , this is the exact same as what were asked to prove
if you go up to the post where I made the assumption step , and expanded out the S(k+1) I wrote there, then you will get the same thing
all summmation induction questions are relatively straight forward, just S(k+1)= S(k) + T(k+1) , know thay and you are good
divisability induction questions are also relatively straight forward, but inequality induction questions are when it starts to get a bit tricky

Not the answer you are looking for?

Search for more explanations.

Ask your own question