math

math

1. handshake

   • 35 hnsahskares. count how much handshakers they cn get ?
     • n(n-1)/2
   • in class of N poeple. how mush handshakers?
     • n(n-1)/2
   • how many dignoals in a pentagon?
     • N(n-1)/2 = provide tota line so without the sides - 5 then (n(n-1)/2)-n
   • how many dignoals in a polygon with n sides

2. seqence

   • 1+2+3+4+........+97+98+99+100
     • add the first with the last to get N
       • N(N-1)/ 2 where n is first and last
     • increases b 1+1+1+1+1+1
   • 1+2+3+4.....+98+99+100+101
     • using N(n-1)/2 + last nmbr
     • increases by 1+1+1+!...
   • 1+2+3+4+.....n
     • using n(n+1)/2 where n/2 is number of pairs
   • 5+6+....99+100
     • assume it starts from 1+2+3+4+5+6.....+99+199 then substruct it from 1+2+3+4
   • 3+5+7+9++.........93+97+99
     • first count number of terms using(( last-first)/ jump up )+1
     • second get number of pairs for each terms
     • third multiply numbr of pairs with N where n the first + last ten ass 99 since its not even
     • it increases by 2+2+2+2+2+

3. patternt

   • traingulat number
     • 1+3+6+10+15.............Th-n
       • it increases by 2+3+4+5+6==== + 1
       • use n * up / 2 so 1*2/2 = 1 which is th number ofseqence dot
         • n(n+1)2
       • pusition 1 2 3 4 5
   • stars
     • 1+4+9+16+........n
       • increases by 3+5+7 === + 2
       • n^2
   • 1 + 2 + 4 + 8 + 16 + 32 + 2^6 + 2^7 + 2^8 + 2^9
     • the ratio can be found by deviding the next with the one befor it
     • it increases by 1 + 2 + 4 + 8 + 16 ===== on +on + on
     • 2^n-1
   • 5 + 11 + 17 + 32 + 29 .........n
     • it increases by 5 +5 + 5+ 5
     • first nmbr + ( n-1) * the increasment
   • 3+12+48+192
     • increases by multiplying the previous term by a constant. = constent = 12/3 = 4 so 4 *3 .4*12 ....
     • nmbr*nmbr ^ n-1
     • needs attintion
   • 2 + 6 + 12 + 20 + 30
     • it increases by on and on and on
     • n(n-1)

4. Sets

   • number of elements == no repeated or order
   • number of subset = 2^number of elemnts
   • number of members in a set = |A| = card(A)
     • A={#,a,5} == Card(a) = 3
     • |A| =3
   • subsets of A | 2^3=8
   • cardinal Numbers = n(S) == number of elemnts in the set with no reapet