Help with Factorial Questions (1 Viewer)

[yleming]

1) Show that k(k!) = (k+1)!-k!

2) Find the largest power of 7 that is a divisor of 100!

3) Express using factorial notation:

a) 30 x 28 x 26 x...x 4 x 2

b) 29 x 27 x 25 x...x 3 x 1

Thanks!

 

[fan96]

1)





Now take out a common factor...

2) Break up into factors. The number of factors of is the amount of times it can be divided by .



How many numbers from 1 to 100 are divisible by 7?

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

There are 14 numbers, but two of these numbers are twice divisible by 7, so count them twice.

Therefore the answer is .