Question:medium

The sum to $n$ terms of the series $\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{7}{8} + \dfrac{15}{16} + \cdots$ is}

Show Hint

For series whose general term can be split, sum each part separately. The geometric part $\sum_{r=1}^n \left(\frac{1}{2}\right)^r = 1 - 2^{-n}$.

Updated On: Apr 8, 2026

$2^{n} - 1$
$1 - 2^{n}$
$n + 2^{n} - 1$
$n - 1 + 2^{-n}$

Show Solution

The Correct Option is D

Solution and Explanation

Was this answer helpful?

Questions Asked in MET exam

Let $ D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} $. Then $ \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} $ is:

MET - 2024
Determinants

View Solution

Given vectors $\vec{a}, \vec{b}, \vec{c}$ are non-collinear and $(\vec{a}+\vec{b})$ is collinear with $(\vec{b}+\vec{c})$ which is collinear with $\vec{a}$, and $|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}$, find $|\vec{a}+\vec{b}+\vec{c}|$.

MET - 2024
Addition of Vectors

View Solution

Given $\frac{dy}{dx} + 2y\tan x = \sin x$, $y=0$ at $x=\frac{\pi}{3}$. If maximum value of $y$ is $1/k$, find $k$.

MET - 2024
Differential equations

View Solution

A real differentiable function $f$ satisfies $f(x)+f(y)+2xy=f(x+y)$. Given $f''(0)=0$, then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]

MET - 2024
Definite Integral

View Solution

The sum to $n$ terms of the series $\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{7}{8} + \dfrac{15}{16} + \cdots$ is}

Show Hint

The Correct Option is D

Solution and Explanation

Top Questions on sequences

Questions Asked in MET exam