lgbasallote
Prove: \[\huge S_n = \frac{n(a_n + a_1)}2\]
Delete
Share
This Question is Closed
lgbasallote
Best Response
You've already chosen the best response.
0
it's an easy proof....but it's still nice to see some professional do it
lgbasallote
Best Response
You've already chosen the best response.
0
i wrote that formula wrong...
vishweshshrimali5
Best Response
You've already chosen the best response.
2
See
\[\S_n = \cfrac{n}{2} (2a + (n-1)d)\]
lgbasallote
Best Response
You've already chosen the best response.
0
and..?
vishweshshrimali5
Best Response
You've already chosen the best response.
2
Now
put
2a +(n-1)d = a + a+(n-1)d = a_1 + a_n
vishweshshrimali5
Best Response
You've already chosen the best response.
2
You get ur answer !
lgbasallote
Best Response
You've already chosen the best response.
0
i don't think that proves anything...that was formula transformation
vishweshshrimali5
Best Response
You've already chosen the best response.
2
see
a_n = a+(n-1)d
vishweshshrimali5
Best Response
You've already chosen the best response.
2
That really does //////////// :)
vishweshshrimali5
Best Response
You've already chosen the best response.
2
You don't want to use the first formula ?
lgbasallote
Best Response
You've already chosen the best response.
0
can you prove a_n = a + (n-1)d?
vishweshshrimali5
Best Response
You've already chosen the best response.
2
I think yes
mathslover
Best Response
You've already chosen the best response.
0
yep
lgbasallote
Best Response
You've already chosen the best response.
0
i think you;re confused....this is proving...not substitution
shubhamsrg
Best Response
You've already chosen the best response.
1
suppose we have
1,2,3,4.....100
adding all, we can see it like this
(1+100) + (2+99) .... ( 50 + 51)
=> (101)*50 = (1 + 100) * (100/2)
you may generalize this..
vishweshshrimali5
Best Response
You've already chosen the best response.
2
And u asked for a proof ;)
lgbasallote
Best Response
You've already chosen the best response.
0
that wasn't a proof @vishweshshrimali5 ....it was formula transformation
lgbasallote
Best Response
You've already chosen the best response.
0
and substitution isn't proving either.... @shubhamsrg
vishweshshrimali5
Best Response
You've already chosen the best response.
2
Whatever........... leave it
I can prove that without using a_n formula
shubhamsrg
Best Response
You've already chosen the best response.
1
substitution ? o.O
vishweshshrimali5
Best Response
You've already chosen the best response.
2
But you will have to accept that a_n = a+(n-1)d
That is basic def. of AP
vishweshshrimali5
Best Response
You've already chosen the best response.
2
I am also surprised @shubhamsrg O.o
shubhamsrg
Best Response
You've already chosen the best response.
1
i am not! ;)
lgbasallote
Best Response
You've already chosen the best response.
0
are any of you familiar with mathematical induction?
vishweshshrimali5
Best Response
You've already chosen the best response.
2
You want that proof........
lgbasallote
Best Response
You've already chosen the best response.
0
what both of you did was substitution (which is NEVER accepted as proofs)
vishweshshrimali5
Best Response
You've already chosen the best response.
2
Let P(n) be the given statement
lgbasallote
Best Response
You've already chosen the best response.
0
no. i want other proof
lgbasallote
Best Response
You've already chosen the best response.
0
induction is too dull and boring and predictable
shubhamsrg
Best Response
You've already chosen the best response.
1
you're amazing you know that ?
shubhamsrg
Best Response
You've already chosen the best response.
1
not you ! ;)
vishweshshrimali5
Best Response
You've already chosen the best response.
2
@lgbasallote
please give us a "hint" of the proof u want
lgbasallote
Best Response
You've already chosen the best response.
0
actually...it's surprising @vishweshshrimali5 does know induction...
shubhamsrg
Best Response
You've already chosen the best response.
1
hint? lol..
lgbasallote
Best Response
You've already chosen the best response.
0
any proof as long as it's valid and not induction
shubhamsrg
Best Response
You've already chosen the best response.
1
induction is one of the many great tools we have in mathematics today!
lgbasallote
Best Response
You've already chosen the best response.
0
preferrably, i like to see direct proof and contradiction
lgbasallote
Best Response
You've already chosen the best response.
0
i like deduction much more
vishweshshrimali5
Best Response
You've already chosen the best response.
2
Ok lets try u want to deduce a formula from a continuous pattern
lgbasallote
Best Response
You've already chosen the best response.
0
time for the site to go down....
mathslover
Best Response
You've already chosen the best response.
0
bye
lgbasallote
Best Response
You've already chosen the best response.
0
so i suppose i'll just ask this again in the fture
vishweshshrimali5
Best Response
You've already chosen the best response.
2
will check out later
mathslover
Best Response
You've already chosen the best response.
0
yep