Sequences and Series

Sequences and Series

1. Sigma Notation

   • Number of terms = n-m+1
   • 1. nΣr=m ( CUr ) = C nΣr=m ( Ur )
   • 3. nΣr=m ( Ur ) = nΣr=k ( Ur ) - m-1Σk ( Ur )
   • 1. nΣr=m ( C ) = ( n-m+1 ) c
   • 2. nΣr=1 ( r ) = n/2 ( 1+n )
   • 3. nΣr=1 ( r^2) = n/6 ( n+1 )(2n+1 )
   • 4. nΣr=1 ( r^3 ) = [ n/2 (1+n ) ]^2
   • 2. nΣr=m ( Ur + Vr ) = nΣr=m ( Ur ) + nΣr=m ( Vr )
   • 5. nΣr=m ( a^r ) = a( a^n -1 ) / a-1 or a( 1- a^n ) / 1-a APGP
   • Un = Sn - Sn-1

2. APGP

   • Un = a + ( n-1 )d
   • Un - Un-1 + constant
   • Sn = n/2 [ 2a + ( n-1 )d] *GP
   • Sn = n/2 ( a+Un )
   • Un = ar^(n-1)
   • Un/ Un-1 = constant
   • Sn = a( 1- r^n )/1-r
   • Sn = a(r^n - 1 )/r-1