contestada

For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 100 terms?
(a) 1
(b) 0
(c) 25
(d) 99/100
(e) 100/101

Respuesta :

Option E is the correct answer.

Step-by-step explanation:

We need to find um of the first 100 terms of

               [tex]\frac{1}{n}-\frac{1}{n+1}[/tex]

That is

           [tex]\texttt{Sum = }\frac{1}{1}-\frac{1}{1+1}+\frac{1}{2}-\frac{1}{2+1}+\frac{1}{3}-\frac{1}{3+1}.....+\frac{1}{100}-\frac{1}{100+1}\\\\\texttt{Sum = }\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}.....+\frac{1}{100}-\frac{1}{101}\\\\\texttt{Sum = }\frac{1}{1}-\frac{1}{101}\\\\\texttt{Sum = }\frac{101-1}{101\times 1}\\\\\texttt{Sum = }\frac{100}{101}[/tex]

Option E is the correct answer.

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