Question
Verify the formula for the value of a telescoping sum:$$\sum_{i=m}^{n}(f(i+1)-f(i))=f(n+1)-f(m)$$Why is the word "telescoping" used to describe this sum?
Step 1
Step 1: First, let's write out the sum in expanded form: $$ \sum_{i=m}^{n}(f(i+1)-f(i)) = (f(m+1)-f(m)) + (f(m+2)-f(m+1)) + \ldots + (f(n+1)-f(n)) $$ Show more…
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