find the sum of .....
1*1! + 2*2! + 3*3! + ....... + 50*50!

Question

find the sum of .....
1*1! + 2*2! + 3*3! + .......  + 50*50!

anonymous · Answer

@Ishaan94  
@apoorvk 
@Mani_Jha 
@experimentX
help????

anonymous · Answer

WBJEE?

apoorvk · Answer

$$T_n = n.n!$$

anonymous · Answer

yup!!!!
there are some sums which i have no idea of!!!

apoorvk · Answer

He's asking all those WBJEE questions which I couldn't solve :D

apoorvk · Answer

@Sarkar Me neither!

anonymous · Answer

But 50! * 50! must be huge.

anonymous · Answer

other ones i was able to solve(11 ones)!!!!,these i got stuck!!!

anonymous · Answer

Magnanmous

anonymous · Answer

$$\large(1!)^2 + (2!)^2 + \ldots + (50!)^2$$

apoorvk · Answer

$$\text{or you can write that as} \frac{(n+1)!}{n}$$


Now what?

apoorvk · Answer

@Ishaan94  it's not n!*n!... read the question again.

anonymous · Answer

guys i got a short trick but dont know if it is possible to apply here.!!!

anonymous · Answer

Ohh yeah

asnaseer · Answer

$$\sum_{n=1}^{50}n.n!=\sum_{n=1}^{50}(n+1)!-n!$$you can use telescoping sum here and see all intermediate sums cancel out leaving just:$$51!-1!$$

asnaseer · Answer

this is using the fact that:$$(n+1)!=(n+1)*n!=n*n!+n!$$

anonymous · Answer

its called cheating....LOL
the series is given till 50!
i did it for shorter series like till
1*1! + 2*2! =3! -1
1*1! + 2*2! + 3*3! =4! - 1
hence if the series is till 
1*1! + 2*2! + 3*3! + .......  + 50*50!
then as per my steps 
it should be 51! - 1

anonymous · Answer

ohh asnaseer haz it. and sarkar too but how do i award medals now?

anonymous · Answer

has*

asnaseer · Answer

give it to Sarkar - I don't mind :)

anonymous · Answer

give it to the one who gave a better thoughtful,strategic ,accurate answer....

asnaseer · Answer

:) - well said Sarkar - just for that you deserve a medal!
but honestly guys I really don't mind who gets medals - I'm on this site for the "joy" of learning and teaching - thats all.

anonymous · Answer

well said@asnaseer and thanks for your explanation....

asnaseer · Answer

yw - I'm glad I was able to help

asnaseer · Answer

BTW: What is WBJEE?

anonymous · Answer

i got another "nagging" Q coming your way in an hours time...

anonymous · Answer

WEST BENGAL JOINT ENTRANCE EXAM

apoorvk · Answer

All Hail @asnaseer and @Sarkar !!

asnaseer · Answer

oh I see - thanks Sarkar
and thanks apoorvk :D