write the sum using sigma notation

Question

Write the sum using sigma notation:

1+2+3+4+......+105= A ∑ n=1 B

A=

B=

 

Answer 1

 

105

∑ n=(n/2)[2a+(n-1)d] where n=105(number of terms),

1

a=1(1st term), and d=1(difference between terms)

 

     =(105/2)[2*1+(105-1)1]

     =(105/2)[2+104]

     =(105/2)[106]

     =(105)(53)

     =5565