displaystyle limn→∞ [(1/1.2) + (1/2.3) + (1/3.4) + .... + (1/n(n+1))] is equal to

Question

displaystyle limn→∞ [(1/1.2) + (1/2.3) + (1/3.4) + .... + (1/n(n+1))] is equal to (A) 1 (B) -1 (C) 0 (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle limn→∞ [(1/1.2) + (1/2.3)+ (1/3.4) +....+ (1/n(n+1))] = displaystyle limn→∞ [ (1-(1/2)) + ((1/2) - (1/3)) +((1/3) -(1/4))+.....+ ((1/n)- (1/n+1))] = displaystyle limn→∞ (1- (1/n+1)) = limn→∞ (n/n+1) = displaystyle limn→∞ (n/n(1+ (1)n)) = limn→∞ (1/(1+ (1)n)) = 1

Q. n→∞lim​[1.21​+2.31​+3.41​+....+n(n+1)1​] is equal to

1

-1

0

None of these

n→∞lim​[1.21​+2.31​+3.41​+....+n(n+1)1​] =n→∞lim​[(1−21​)+(21​−31​)+(31​−41​)+.....+(n1​−n+11​)] =n→∞lim​(1−n+11​)=n→∞lim​n+1n​ =n→∞lim​n(1+n1​)n​=n→∞lim​(1+n1​)1​=1

Q. $n \to \infty lim [\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + .... + \frac{1}{n ( n + 1 )}]$ is equal to