Question

Need an answer showing work thax!

Answer 1

Answer:

Option (a) $\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}$

Step-by-step explanation:

The given expression is :

$\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....$

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

$\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}$

Hence, the correct option is (A).