lgbasallote 3 years ago Prove: $\huge S_n = \frac{n(a_n + a_1)}2$

1. lgbasallote

it's an easy proof....but it's still nice to see some professional do it

2. lgbasallote

i wrote that formula wrong...

3. vishweshshrimali5

See $\S_n = \cfrac{n}{2} (2a + (n-1)d)$

4. lgbasallote

and..?

5. vishweshshrimali5

Now put 2a +(n-1)d = a + a+(n-1)d = a_1 + a_n

6. vishweshshrimali5

7. lgbasallote

i don't think that proves anything...that was formula transformation

8. vishweshshrimali5

see a_n = a+(n-1)d

9. vishweshshrimali5

That really does //////////// :)

10. vishweshshrimali5

You don't want to use the first formula ?

11. lgbasallote

can you prove a_n = a + (n-1)d?

12. vishweshshrimali5

I think yes

13. mathslover

yep

14. lgbasallote

i think you;re confused....this is proving...not substitution

15. 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..

16. vishweshshrimali5

And u asked for a proof ;)

17. lgbasallote

that wasn't a proof @vishweshshrimali5 ....it was formula transformation

18. lgbasallote

and substitution isn't proving either.... @shubhamsrg

19. vishweshshrimali5

Whatever........... leave it I can prove that without using a_n formula

20. shubhamsrg

substitution ? o.O

21. vishweshshrimali5

But you will have to accept that a_n = a+(n-1)d That is basic def. of AP

22. vishweshshrimali5

I am also surprised @shubhamsrg O.o

23. shubhamsrg

i am not! ;)

24. vishweshshrimali5

;)

25. lgbasallote

are any of you familiar with mathematical induction?

26. vishweshshrimali5

Yes

27. vishweshshrimali5

You want that proof........

28. lgbasallote

what both of you did was substitution (which is NEVER accepted as proofs)

29. vishweshshrimali5

Let P(n) be the given statement

30. lgbasallote

no. i want other proof

31. lgbasallote

induction is too dull and boring and predictable

32. shubhamsrg

you're amazing you know that ?

33. shubhamsrg

not you ! ;)

34. vishweshshrimali5

@lgbasallote please give us a "hint" of the proof u want

35. lgbasallote

actually...it's surprising @vishweshshrimali5 does know induction...

36. shubhamsrg

hint? lol..

37. lgbasallote

any proof as long as it's valid and not induction

38. shubhamsrg

induction is one of the many great tools we have in mathematics today!

39. lgbasallote

preferrably, i like to see direct proof and contradiction

40. lgbasallote

i like deduction much more

41. vishweshshrimali5

Ok lets try u want to deduce a formula from a continuous pattern

42. lgbasallote

time for the site to go down....

43. mathslover

bye

44. vishweshshrimali5

bye

45. lgbasallote

so i suppose i'll just ask this again in the fture

46. vishweshshrimali5

will check out later

47. mathslover

yep