Question #274087

What are the values of the following expressions?

  • ∑_(i=3)^6▒ (i^2+6)
  • ∏_(j=1)^5▒ (j/2)
  • 4!
  • 0!
  • (6¦2)
  • C(6,2)
1
Expert's answer
2021-12-01T18:23:01-0500

(i)


i=36(i2+6)=32+6+42+6+52+6+62+6\displaystyle\sum_{i=3}^6(i^2+6)=3^2+6+4^2+6+5^2+6+6^2+6

=110=110

(ii)


j=15(i/2)=1(2)(3)(4)(5)2(2)(2)(2)(2)=154\displaystyle\prod_{j=1}^5(i/2)=\dfrac{1(2)(3)(4)(5)}{2(2)(2)(2)(2)}=\dfrac{15}{4}

(iii)


4!=1(2)(3)(4)=244!=1(2)(3)(4)=24

(iv)


0!=10!=1

(v)


P(6,2)=6!(62)!=6(5)=30P(6, 2)=\dfrac{6!}{(6-2)!}=6(5)=30

(vi)


C(6,2)=6!2!(62)!=6(5)1(2)=15C(6, 2)=\dfrac{6!}{2!(6-2)!}=\dfrac{6(5)}{1(2)}=15


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