Question #fedb7

2 Answers
P dilip_k
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!#

P dilip_k
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!#

Related questions
See all questions in Multiplication of Rational Expressions
Impact of this question
2594 views around the world
You can reuse this answer
Creative Commons License