lgbasallote
  • lgbasallote
Prove: \[\huge S_n = \frac{n(a_n + a_1)}2\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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lgbasallote
  • lgbasallote
it's an easy proof....but it's still nice to see some professional do it
lgbasallote
  • lgbasallote
i wrote that formula wrong...
vishweshshrimali5
  • vishweshshrimali5
See \[\S_n = \cfrac{n}{2} (2a + (n-1)d)\]

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lgbasallote
  • lgbasallote
and..?
vishweshshrimali5
  • vishweshshrimali5
Now put 2a +(n-1)d = a + a+(n-1)d = a_1 + a_n
vishweshshrimali5
  • vishweshshrimali5
You get ur answer !
lgbasallote
  • lgbasallote
i don't think that proves anything...that was formula transformation
vishweshshrimali5
  • vishweshshrimali5
see a_n = a+(n-1)d
vishweshshrimali5
  • vishweshshrimali5
That really does //////////// :)
vishweshshrimali5
  • vishweshshrimali5
You don't want to use the first formula ?
lgbasallote
  • lgbasallote
can you prove a_n = a + (n-1)d?
vishweshshrimali5
  • vishweshshrimali5
I think yes
mathslover
  • mathslover
yep
lgbasallote
  • lgbasallote
i think you;re confused....this is proving...not substitution
shubhamsrg
  • shubhamsrg
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
  • vishweshshrimali5
And u asked for a proof ;)
lgbasallote
  • lgbasallote
that wasn't a proof @vishweshshrimali5 ....it was formula transformation
lgbasallote
  • lgbasallote
and substitution isn't proving either.... @shubhamsrg
vishweshshrimali5
  • vishweshshrimali5
Whatever........... leave it I can prove that without using a_n formula
shubhamsrg
  • shubhamsrg
substitution ? o.O
vishweshshrimali5
  • vishweshshrimali5
But you will have to accept that a_n = a+(n-1)d That is basic def. of AP
vishweshshrimali5
  • vishweshshrimali5
I am also surprised @shubhamsrg O.o
shubhamsrg
  • shubhamsrg
i am not! ;)
vishweshshrimali5
  • vishweshshrimali5
;)
lgbasallote
  • lgbasallote
are any of you familiar with mathematical induction?
vishweshshrimali5
  • vishweshshrimali5
Yes
vishweshshrimali5
  • vishweshshrimali5
You want that proof........
lgbasallote
  • lgbasallote
what both of you did was substitution (which is NEVER accepted as proofs)
vishweshshrimali5
  • vishweshshrimali5
Let P(n) be the given statement
lgbasallote
  • lgbasallote
no. i want other proof
lgbasallote
  • lgbasallote
induction is too dull and boring and predictable
shubhamsrg
  • shubhamsrg
you're amazing you know that ?
shubhamsrg
  • shubhamsrg
not you ! ;)
vishweshshrimali5
  • vishweshshrimali5
@lgbasallote please give us a "hint" of the proof u want
lgbasallote
  • lgbasallote
actually...it's surprising @vishweshshrimali5 does know induction...
shubhamsrg
  • shubhamsrg
hint? lol..
lgbasallote
  • lgbasallote
any proof as long as it's valid and not induction
shubhamsrg
  • shubhamsrg
induction is one of the many great tools we have in mathematics today!
lgbasallote
  • lgbasallote
preferrably, i like to see direct proof and contradiction
lgbasallote
  • lgbasallote
i like deduction much more
vishweshshrimali5
  • vishweshshrimali5
Ok lets try u want to deduce a formula from a continuous pattern
lgbasallote
  • lgbasallote
time for the site to go down....
mathslover
  • mathslover
bye
vishweshshrimali5
  • vishweshshrimali5
bye
lgbasallote
  • lgbasallote
so i suppose i'll just ask this again in the fture
vishweshshrimali5
  • vishweshshrimali5
will check out later
mathslover
  • mathslover
yep

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