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$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is

1. $2$
2. $1$
3. $\infty$
4. not a convergent series

recategorized | 17 views

Answer is B instead of infinity just take 99 then i can write 1/n(n+1) as 1/n-1/n+1 if you write like this middle terms will cancel only first and last term will remain 1-1/100 so 99/100 so 0.99 similarly if you take 999 sum wil be 0.999 so on for infinity it wil be 0.99999.....=1 so 1 is the answer.
by Junior (841 points)