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labwork [276]
3 years ago
12

Find the sum: 1+2+3+ ... +9999+10000.

Mathematics
2 answers:
Elza [17]3 years ago
5 0
This requires the formula for summation of an arithmetic sequence, which was first derived by Gauss, since the sequence is of the form u_{n} = n.

a = 1 (the first term)
L = 10000 (the last term)
n = 10000 (the number of terms summed)

The formula is:
S = \frac{1}{2}n(a + L)
S = ( \frac{1}{2}*10000)(1 + 10000) = 50005000

Therefore the sum is 50005000

I hope this helps
Strike441 [17]3 years ago
3 0
It's an arithmetic sequence.

1,2,3,...,9999,10000 \\ \\
a_1=1 \\
d=a_2-a_1=2-1=1

Find which term is 10000:
a_n=a_1+d(n-1) \\
10 000=1+1(n-1) \\
10000=1+n-1 \\
n=10000
10000 is the 10000th term.

S_n=\frac{n(a_1+a_n)}{2} \\
\Downarrow \\
S_{10 000}=\frac{10 000(1+10 000)}{2}=\fra{10 000 \times 10 001}{2}=5 000 \times 10 001=50005000 \\ \\
\boxed{1+2+3+...+9999+10000=50005000}
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Alexxandr [17]

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padilas [110]

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A

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2 years ago
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Ahat [919]

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B

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Weekly salary: $650; earnings to date: $30,000.​
Anuta_ua [19.1K]

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