IIT JEE , AIEEE Forum - Mathematics , Algebra

nvphadnis

find the nth term and summation upto n terms :
1/{(x+1)(x+2)(x+3)}

konichiwa2x

You have been given the nth term!

Notice that all terms except the 1st and the last in the above step cancel out.

nvphadnis

but won't the nth term be :

1/{(x+n)(x+n+1)(x+n+2)}

according to the formula Tn = a+(n-1)d
where d=1 and a=x+1,x+2 & x+3 ?

konichiwa2x

buddy, you need to be clear about the question.

Which of the below is the sum you need? I have provided the solution above for the 2nd one.

or

?

konichiwa2x

ok this is the answer if you meant the first option.

Once again notice that all the terms except the first and the last get cancelled,

.

Notice that if you substitute x = 1, you get the sum for the 2nd problem!

Cheers!