Question #fedb7

2 Answers
Nov 29, 2016

Let r th term of the given series

t_r=r*r! =(r+1-1)r! =(r+1)!-r!

putting r=1,2,3.4....100

1*1! =2!-1!

2*2! =3!-2!

3*3! =4!-3!

----------

----------

99*99! =100!-99!

100*100! =101!-100!

So adding these we get required sum

S=101!-1!

Nov 29, 2016

Let r th term of the given series

t_r=r*r! =(r+1-1)r! =(r+1)!-r!

putting r=1,2,3.4....100

1*1! =2!-1!

2*2! =3!-2!

3*3! =4!-3!

----------

----------

99*99! =100!-99!

100*100! =101!-100!

So adding these we get required sum

S=101!-1!