Question

(1/2+1/3.....1/2008) (1+1/2+1/3+.....2007)-(1+1/2+1/3.....1/2008)(1/2+1/3.....1/2007)=k/2008 find k

Answer 1

Given: (1/2+1/3.....1/2008) (1+1/2+1/3+.....2007)-(1+1/2+1/3.....1/2008)(1/2+1/3.....1/2007)=k/2008

To find: The value of k?

Solution:

• Now we have given :

              (1/2+1/3.....1/2008) (1+1/2+1/3+.....2007)-(1+1/2+1/3.....1/2008)(1/2+1/3.....1/2007) = k/2008

• Consider LHS, we have :

              (1/2+1/3.....1/2008) (1+1/2+1/3+.....2007)-(1+1/2+1/3.....1/2008)(1/2+1/3.....1/2007)

• Let a = (1/2+1/3.....1/2008)

              b = (1/2+1/3.....1/2007)

• So putting a and b in given equation, we get:

              a(1 + b) - (1 + a)(b)

• Now expanding it, we get:

              a + ab - b - ab

              a - b

• Putting the values we get:

              (1/2+1/3.....1/2008) - (1/2+1/3.....1/2007)

• Now all the terms will get cancelled except 1/2008, so:

              a - b = 1/2008 = k/2008

              k = 1

Answer:

           So the value of k is 1.