Question

TELESCOPING TRICK for n/(n+1) ) to obtain two terms
a) True
b) False

Answer 1

The telescoping trick is a method used in mathematics to collapse a series into fewer terms by canceling out many intermediate terms. It can be applied to the series of fractions n/(n+1), leading to a simplified expression of two terms, confirming the statement as True.

Step-by-step explanation:

The question appears to be about using a telescoping trick to simplify a series expansion involving fractions of the form n/(n+1). This is a technique often used in mathematics to find the sum of a series by exploiting the cancellation of terms. The technique works by rewriting each fraction so that when we add them, many terms cancel out. In the context of the question, let's consider the sum of such fractions:

• 1/(1+1) + 2/(2+1) + ... + n/(n+1)

We can rewrite each fraction as:

(n/(n+1)) = 1 - (1/(n+1))

When we add these up, the -1/(n+1) from one term will cancel with the 1 from the subsequent term, leading to a telescoping sum which collapses down to:

• 1 - 1/(2) + 1 - 1/(3) + ... + 1 - 1/(n+1)

Upon cancellation:

• 1 - 1/(n+1)

Thus, for the fraction n/(n+1), using the telescoping method, we arrive at two terms, which confirms the statement as True.