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Question

The sum to infinity of the given series $fraction numerator 1 over denominator n end fraction minus fraction numerator 1 over denominator 2 n to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 n to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 4 n to the power of 4 end exponent end fraction plus....$ is

$\log_{e} (\frac{n + 1}{n})$
$\log_{e} (\frac{n}{n + 1})$
$\log_{e} (\frac{n - 1}{n})$
$\log_{e} (\frac{n}{n - 1})$

The correct answer is: $log subscript e end subscript invisible function application open parentheses fraction numerator n plus 1 over denominator n end fraction close parentheses$

$fraction numerator 1 over denominator n end fraction minus fraction numerator 1 over denominator 2 n to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 n to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 4 n to the power of 4 end exponent end fraction plus....$
$equals fraction numerator 1 over denominator n end fraction minus fraction numerator left parenthesis 1 divided by n right parenthesis to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator left parenthesis 1 divided by n right parenthesis to the power of 3 end exponent over denominator 3 end fraction minus fraction numerator left parenthesis 1 divided by n right parenthesis to the power of 4 end exponent over denominator 4 end fraction plus....$
$equals log subscript e end subscript invisible function application open parentheses 1 plus fraction numerator 1 over denominator n end fraction close parentheses equals log subscript e end subscript invisible function application open parentheses fraction numerator n plus 1 over denominator n end fraction close parentheses$

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

Maths-General

General

Maths-

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

Maths-General

General

Maths-

$fraction numerator 1 over denominator 5 end fraction plus fraction numerator 1 over denominator 2 end fraction. fraction numerator 1 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 end fraction. fraction numerator 1 over denominator 5 to the power of 3 end exponent end fraction plus..... infinity equals$

Maths-General

General

Physics-

White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

Physics-General

General

Biology

The sum of 730 + 450 using front – end estimation is______.

Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.

The sum of 730 + 450 using front – end estimation is______.

Maths-General

Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.

General

Maths-Video

Round the number 5432 to the nearest hundred.

For rounding off to the nearest hundred, we can also look at the number formed by the tens place digit and one place digit. If the number formed is less than 50,we round down and if the number is 50 or more we round up.

Round the number 5432 to the nearest hundred.

Maths-General

General

GeneralVideo

Estimate 275 + 238 to nearest hundred.

GeneralGeneral

General

Mathematics

What is the value of 20/100?

MathematicsGeneral

General

Biology

Identify structures A to D –

BiologyGeneral

General

botany-

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

botany-General

General

botany-

If there are exactly two points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ whose distance from its centre is same and is equal to $square root of fraction numerator a to the power of 2 end exponent plus 2 b to the power of 2 end exponent over denominator 2 end fraction end root$ then eccentricity of the ellipse is

botany-General

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The sum to infinity of the given series is

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Related Questions to study

is defined for

is defined for

The sum of the series

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White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

Which of the following is less general in characters as compared to genus?

Which of the following is less general in characters as compared to genus?

For which of the following motions gravity is not responsible?

For which of the following motions gravity is not responsible?

The velocity-time graph of a uniformly decelerating motion is a ____.

The velocity-time graph of a uniformly decelerating motion is a ____.

Sepia is also known as

Sepia is also known as

The sum of 730 + 450 using front – end estimation is______.

The sum of 730 + 450 using front – end estimation is______.

Round the number 5432 to the nearest hundred.

Round the number 5432 to the nearest hundred.

Estimate 275 + 238 to nearest hundred.

Estimate 275 + 238 to nearest hundred.

What is the value of 20/100?

What is the value of 20/100?

Identify structures A to D –

Identify structures A to D –

An ellipse slides between two perpendicular straight lines then, locus of its foci is

An ellipse slides between two perpendicular straight lines then, locus of its foci is

If there are exactly two points on the ellipse whose distance from its centre is same and is equal to then eccentricity of the ellipse is

If there are exactly two points on the ellipse whose distance from its centre is same and is equal to then eccentricity of the ellipse is

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The correct answer is: $log subscript e end subscript invisible function application open parentheses fraction numerator n plus 1 over denominator n end fraction close parentheses$

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is