Question

100(1+100)
Example : 1+2+3+…+100= -----------
2

Simplify: (x+1) + 2(x+1)+ …+1000(x+1)

Answer 1

If you in google type:
Sum of numbers 1 to 100


By the way:

1 + 2 + 3 + 4 + . . . . + n = ( 1 + n )*( n / 2 )


1 + 2 + 3 +…100

n = 100

1 + 2 + 3 +…100 =( 1 + 100 ) * ( 100 / 2 ) = 101 * 50 = 5050


( x + 1 ) + 2 ( x + 1) + …+ 1000 ( x + 1 ) = ( x + 1 ) ( 1 + 2 +...1000 )

n = 1000

1 + 2 +....1000 = ( 1 + 1000 ) ( 1000 / 2 ) = 1001 * 500 = 500500


( x + 1 ) + 2 ( x + 1) + …+ 1000 ( x + 1 ) =

( x + 1 ) ( 1 + 2 +...1000 ) =

( x + 1 ) * 500500 = 505050 ( x + 1 )

Answer 2

( x + 1 ) * 500500 = 500500 ( x + 1 )