Mathematics

# $\sum\limits_{r = 1}^n r {\left( {1 + \frac{1}{n}} \right)^{r - 1}}$ is equal to

$2{n^2}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle\int { \frac { \cos { 4x } +1 }{ \cot { x } -\tan { x } } } dx=A\cos { 4x } +B$; where $A$ & $B$ are constants, then
• A. $A=-1/4$ & $B$ may have any value
• B. $A=-1/2$ & $B=-1/4$
• C. $A=B=1/2$
• D. $A=-1/8$ & $B$ may have any value

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle\int _{ 0 }^{ \pi /2 }{ \sin ^{ 6 }{ x } } dx$ is
• A. $\cfrac{5\pi}{16}$
• B. $\cfrac{5\pi}{64}$
• C. $\cfrac{5\pi}{8}$
• D. $\cfrac{5\pi}{32}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve:
$\displaystyle \int \dfrac{2\cos x}{(1-\sin x)(1+\sin ^2x)}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find the value of $\int xe^x \, dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
If $\displaystyle \int { \frac { { e }^{ x }-1 }{ { e }^{ x }+1 } dx } =f\left( x \right) +C$, then $f\left( x \right)$ is equal to
• A. $\log { \left( { e }^{ 2x }-1 \right) }$
• B. $2\log { \left( { e }^{ x }+1 \right) } -x$
• C. $\log { \left( { e }^{ x }-1 \right) }$
• D. $2\log { \left( { e }^{ x }+1 \right) }$