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angeles86
13.08.2020 •
Mathematics
Use the trick of Gauss to add up consecutive integers from 111 to 200200200, that is, find the sum 1+2+3+…+199+200 .\qquad\qquad\qquad 1+2+3+\ldots+199+200\;.1+2+3+…+199+200.
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Ответ:
20100
Step-by-step explanation:
To find the sum of:
As per the trick of Gauss, let us divide the above terms in two halves.
Let us re rewrite the above terms by reversing the second sequence of terms.
Adding the corresponding terms (it will also contain 100 terms):
1 + 200 = 201
2 + 199 = 201
3 + 198 = 201
:
:
100 + 101 = 201
The number of terms in each sequence are 100.
So, we have to add 201 for 100 times to get the required sum.
Required sum = 201 + 201 + 201 + 201 + . . . + 201 (100 times)
Required sum = 100
201 = 20100
Ответ:
no
Step-by-step explanation: