If ⁻¹ [ 1 1+1.2 ]+ ⁻¹ [ 1 1+2.3 ]+ + ⁻¹ [ 1 1+n(n+1) ]= ⁻¹[x] , then x is equal to

Step-by-step solution

aligned & Given ⁻¹ ( 1 1+1.2 )+ ⁻¹ ( 1 1+2.3 )+ & + ⁻¹ ( 1 1+n(n+1) )= ⁻¹(x) aligned aligned ⁻¹ ( 2-1 1+1.2 ) & + ⁻¹ ( 3-2 1+2.3 )+ & + ⁻¹ ( n+1-n 1+n(n+1) )= ⁻¹(x) aligned aligned & ⁻¹(2)- ⁻¹(1)+ ⁻¹(3)- ⁻¹(2)+ & + ⁻¹( n +1)- ⁻¹( n )= ⁻¹(x) aligned ⁻¹( n +1)- ⁻¹(1)= ⁻¹(x) ⁻¹(A)- ⁻¹(B)= ⁻¹ ( A-B 1+A B ) ⁻¹ ( n n+2 )= ⁻¹(x) x= n n+2