how to do problem like the following super fast? 99+98+97+96...+2+1/99!

Question

Steps to solve the question please.

 

99+98+97...+2+1/99 factorial

Answer 1

if there is no typo...

 

(99+98+97+..+3+2+1)/99!

working with the numerator first

there are 99 consecutive integers

the middle one is 50

99+1=100

98+2=100

97+3=100

etc

there are 49 groups of 100 (2*49=98 integers plus the middle one which is 50)

49*100+50=4950

4950/99! is what you have so far

4950=50*99

(50)(99)/(99*98*97*...*50*...3*2*1)

simplify by factoring out 50 and 99 from both the numerator and the denominator

1/(98*97*96*...*51*49*48*...*3*2*1)

 

Answer 2

First off, John, factorial is the product, not the sum.

 

99 + 1 = 100

98 + 2 = 100

 

Can you figure it out now?