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3 years ago

Find the sum of (1-1/n) + (1-2/n) + (1 - 3/n)....upto n terms

Mathematics

1 answer:

bija089 [108]3 years ago

4 0

Answer:

(n - 1)/2

Step-by-step explanation:

F = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) + ...(1 - n/n)

= (1 + 1 ... + 1) - (1/n + 2/n + 3/n + ...n/n)

(there are n terms of 1)

= n - (1 + 2 + 3 + ... + n)/n

= n - [n x (n + 1)/2]/n

= n - [n x (n + 1)]/[2 x n]

= n - (n+1)/2

= (2n - n - 1)/2

= (n - 1)/2

Hope this helps!

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Answer:

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Step-by-step explanation:

Given:

The numbers to order from least to greatest is given as:

$-5.5, 4.5, 22/7,\sqrt4,-\sqrt{20}$

In order to compare these numbers, we have to convert them in same form.

Let us simplify each number in decimal form.

$-5.5 = -5.5\\\\4.5=4.5\\\\\frac{22}{7}=3.14\\\\\sqrt4=2\\\\-\sqrt{20}=-\sqrt{5\times 2^2}=-2\sqrt5=-4.47$

So, the least number is one which has the largest value with a negative sign.

Here, -5.5 is the least number.

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The next smallest number is 2. So, $\sqrt4$

The next smallest number is 3.14. So, $\frac{22}{7}$

The greatest number is 4.5.

Therefore, the order from the least to greatest is:

-5.5 < $-\sqrt{20}$ < $\sqrt4$ < $\frac{22}{7}$ < 4.5

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