Question
Find the sum of first n natural numbers.
✓
Answer
The first n natural numbers are 1, 2, 3, 4, 5, ..., n.
Here, a = 1 and d = (2 - 1) = 1
Sum of n terms of an AP is given by
$\text{S}_\text{n}=\frac{\text{n}}{2}\big[2\text{a}+(\text{n}-1)\text{d}\big]$
$=\big(\frac{\text{n}}{2}\big)\times\big[2\times1+(\text{n}-1)\times1\big]$
$=\big(\frac{\text{n}}{2}\big)\times\big[2+\text{n}-1\big]=\big(\frac{\text{n}}{2}\big)\times(\text{n}+1)=\frac{\text{n}(\text{n}+1)}{2}$
Here, a = 1 and d = (2 - 1) = 1
Sum of n terms of an AP is given by
$\text{S}_\text{n}=\frac{\text{n}}{2}\big[2\text{a}+(\text{n}-1)\text{d}\big]$
$=\big(\frac{\text{n}}{2}\big)\times\big[2\times1+(\text{n}-1)\times1\big]$
$=\big(\frac{\text{n}}{2}\big)\times\big[2+\text{n}-1\big]=\big(\frac{\text{n}}{2}\big)\times(\text{n}+1)=\frac{\text{n}(\text{n}+1)}{2}$
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Solve for x and y:
$\frac{35}{\text{x}+\text{y}}+\frac{14}{\text{x}-\text{y}}=19,$ $\frac{14}{\text{x}+\text{y}}+\frac{35}{\text{x}-\text{y}}=37$
→$\frac{35}{\text{x}+\text{y}}+\frac{14}{\text{x}-\text{y}}=19,$ $\frac{14}{\text{x}+\text{y}}+\frac{35}{\text{x}-\text{y}}=37$
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1, 2, 3, ....., 12 as shown in following figure. What is the probability that it will point to:
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