We will use demonstration of recurrences<span>1) for n=1, 10= 5*1(1+1)=5*2=10, it is just
2) assume that the equation </span>10 + 30 + 60 + ... + 10n = 5n(n + 1) is true, <span>for all positive integers n>=1
</span>3) let's show that the equation<span> is also true for n+1, n>=1
</span><span>10 + 30 + 60 + ... + 10(n+1) = 5(n+1)(n + 2)
</span>let be N=n+1, N is integer because of n+1, so we have
<span>10 + 30 + 60 + ... + 10N = 5N(N+1), it is true according 2)
</span>so the equation<span> is also true for n+1,
</span>finally, 10 + 30 + 60 + ... + 10n = 5n(n + 1) is always true for all positive integers n.
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10 students of Elena's classmates like to make jewellery.
<u>Step-by-step explanation:</u>
Let total no.of classmates who liked the jewellery = x
Here, in the given problem, given she asked her classmates '20'. So, it clearly shows that total number of students/classmates = 20. Also, in that, 50% said like to make jewellery. Now find 'x' as below,



Hence, the total number of classmates who liked to make Jewellery = 10
Answer:
here
Step-by-step explanation:
The x^2 over the x is like subtracting x from x^2, so the new equation would be 9-x/-3. You divide 9 by -3 to get the final answer of -3-x, or -x-3, which is E.