Question

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

Answer 1

Option E is the correct answer.

Explanation:

We need to find um of the first 100 terms of

`(1)/(n)-(1)/(n+1)`

That is

`\texttt{Sum = }(1)/(1)-(1)/(1+1)+(1)/(2)-(1)/(2+1)+(1)/(3)-(1)/(3+1).....+(1)/(100)-(1)/(100+1)\\\\\texttt{Sum = }(1)/(1)-(1)/(2)+(1)/(2)-(1)/(3)+(1)/(3)-(1)/(4).....+(1)/(100)-(1)/(101)\\\\\texttt{Sum = }(1)/(1)-(1)/(101)\\\\\texttt{Sum = }(101-1)/(101* 1)\\\\\texttt{Sum = }(100)/(101)`

Option E is the correct answer.