Sum of the series n1x1-1x2-1xn is a-

The correct option is D harmonic meanLet n numbers be: x_1, x_2, x_3,.....,x_n ∴ A.M. = x_1+ x_2+ x_3+.....+x_nn ∴ G.M. = (x_1.x_2.x_3..... ...

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Standard XII

Mathematics

Harmonic Mean

Sum of the se...

Question

Sum of the series $\frac{n}{\frac{1}{x_{1}} + \frac{1}{x_{2}} . . . + \frac{1}{x_{n}}}$ is a:

arithmetic mean

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geometric mean

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arithmetic series

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harmonic mean

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Solution

The correct option is D harmonic mean
Let $n$ numbers be:
$x_{1}, x_{2}, x_{3}, . . . . ., x_{n}$

$∴ A . M . = \frac{x_{1} + x_{2} + x_{3} + . . . . . + x_{n}}{n}$

$∴ G . M . = (x_{1} . x_{2} . x_{3} . . . . . . x_{n})^{\frac{1}{n}}$

$∴ H . M . = \frac{n}{\frac{1}{x_{1}} + \frac{1}{x_{2}} + \frac{1}{x_{3}} + . . . . . + \frac{1}{x_{n}}}$

Hence, the answer is harmonic mean.

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Sum of the series n1x1+1x2...+1xn is a:

The correct option is D harmonic meanLet n numbers be:x1,x2,x3,.....,xn∴A.M.=x1+x2+x3+.....+xnn∴G.M.=(x1.x2.x3......xn)1n∴H.M.=n1x1+1x2+1x3+.....+1xnHence, the answer is harmonic mean.

Sum of the series $\frac{n}{\frac{1}{x_{1}} + \frac{1}{x_{2}} . . . + \frac{1}{x_{n}}}$ is a: