Question

Homework Time. Can anyone help me with just getting started? Well it say find the sum 1+3+5...(2n-1). Okay how i suppose to do this?

Answer 1

do you know how to find the sum of 1+2+3+...+n ?

Answer 2

Yes you use the formula nut whats making it hard is the (2n-1)

Answer 3

we can do this "trick" (or neat idea, depending on your point of view)
we can add 0 to each term (adding 0 won't change the answer, right?) where 0= -1+1
so
1 -1 +1 +3 -1 +1 +5 -1+1 + ....+ 2n-1 -1 +1

Answer 4

But why are you subtracting 1 when its just asking to find the sum. I'm just lost on how to get rid of the formula

Answer 5

now simplify it a bit:
1 -1 +1 +3 -1 +1 +5 -1+1 + ....+ 2n-1 -1 +1
0 +1 +2 +1 + 4 +1 .... + 2n-2 +1

now we have
0+2+4+...+ 2(n-1)
(picking out the 0,2,4 numbers)

and 1+1+1+...+1 (we have to figure out how many 1's)

follow ?

Answer 6

this part of the problem
0+2+4+...+ 2(n-1)
we can factor out 2 from each term to get
2(1+2+3...+(n-1) )
and you know how to do the sum inside the parens

Answer 7

trying to follow but your kind of confusing me with the subtracting one. Unless you subtracting it from the formula... Bot do you know an simpler way instead of subtracting one

Answer 8

Try this idea
you have
1 + 3 + 5+7 + .... + (2n-1)
write this as
1 + (2+1) + (4+1) + (6+1) + .... + (2n-2 + 1)
(almost the same idea. we break the 3 into 2+1, the 5 into 4+1 and so on)

so we have a bunch of 1's and 2+4+6+..+2(n-1)
and (just like before)
2+4+6+..+2(n-1)= 2(1+2+3+...+(n-1))

Answer 9

So will this let me find the sum of them all

Answer 10

you have n terms in the original problem (takes some thinking to show this)
so you have n 1's which add up to n
and
you have 2* sum(1...(n-1))
sum(1..(n-1))= (n-1)*n/2
times 2, you get (n-1)*n

so the answer is n (from the ones) + n*(n-1)
n+n(n-1)