The n^{th} term of the series frac{1}{1} + fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given series is $\frac{1}{1} + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + \dots$The $n^{th}$ term of the series is given by the sum of the first

Vedclass · Accepted Answer

$\frac{n + 1}{2}$

Vedclass · Answer

(A) The given series is $\frac{1}{1} + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + \dots$The $n^{th}$ term of the series is given by the sum of the first $n$ natural numbers divided by $n$.$T_n = \frac{1 + 2 + 3 + \dots + n}{n}$Using the formula for the sum of the first $n$ natural numbers,$\sum_{k=1}^{n} k = \frac{n(n + 1)}{2}$,we get:$T_n = \frac{\frac{n(n + 1)}{2}}{n}$$T_n = \frac{n(n + 1)}{2n}$$T_n = \frac{n + 1}{2}$Thus,the correct option is $A$.

The $n^{th}$ term of the series $\frac{1}{1} + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + \dots$ will be

Similar Questions

The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is

If $A = 1 + r^z + r^{2z} + r^{3z} + .......\infty$,then the value of $r$ will be

If $a_1, a_2, a_3, \dots$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first $15$ terms of this $A.P.$ is

If $\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \dots + \infty = \frac{\pi^4}{90}$,then the value of $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \dots + \infty$ is

The sum of the first and third term of an arithmetic progression is $12$ and the product of the first and second term is $24$. Find the first term.

Vedclass Test Series

Exam Paper Generator

Online Exam Module