Consider a sequence of number a_{1}, a_{2}, a_{3} . . ., a_{n} where a_{n}=\frac{1}{n}-\frac{1}{n+2}, for each integer n>0 . What is the sum of the first 50 terms?

Correct Answer is : (1+12)−(151+152)

(1+\frac{1}{2})-(\frac{1}{51}+\frac{1}{52})

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 6 of 65

Marks: +1, -0

Consider a sequence of number

a_{1}, a_{2}, a_{3} . . ., a_{n} \;\;

where

\;\; a_{n}=\;{1}/{n}-\;{1}/{n+2}

, for each integer

n>0 .

What is the sum of the first 50 terms?

Solution:

Sum of series will

(1-\;{1}/{3})+(\;{1}/{2}-\;{1}/{4})+(\;{1}/{3}-\;{1}/{5}) ⋅s(\;{1}/{48}-\;{1}/{50})+

(\;{1}/{49}-\;{1}/{51})+(\;{1}/{50}-\;{1}/{52})

All like terms will cancel out and we will be left with

(1+\;{1}/{2})-(\;{1}/{51}+\;{1}/{52})

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