Find the sum sigma3k 0 1k Leave your answer in the form of

Find the sum sigma^3_k = 0 1/k!. Leave your answer in the form of a single fraction.

Solution

_{[k=0 to 3]} (1_/k!)   

=(1_/0!) +(1_/1!) +(1_/2!) +(1_/3!)   

=(1_/1) +(1_/1) +(1_/2) +(1_/6)   

=1 +1 +(1_/2) +(1_/6)   

=2 +(1_/2) +(1_/6)   

=((2*6)+(1*3)+1)_/6

=(12+3+1)_/6

=16_/6

=8_/3