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Консультация № 190711
16.03.2017, 17:13
0.00 руб.
0
4
3
Здравствуйте! У меня возникли сложности с таким вопросом:
Какой цифрой оканчивается сумма всех двузначных чисел?
Какой цифрой оканчивается сумма всех двузначных чисел?
Обсуждение
16.03.2017, 17:29
общий
это ответ
Здравствуйте, svrvsvrv!
Последние цифры 0+(1+9)+(2+8)+(3+7)+(4+6) дадут 0
На результат повлияют только последние пятерки. Таких чисел 9 (15, 25,...,95), т.е. нечетное количество, их сумма закончится на 5.
Вывод: Сумма всех двузначных чисел закончится на 5
Последние цифры 0+(1+9)+(2+8)+(3+7)+(4+6) дадут 0
На результат повлияют только последние пятерки. Таких чисел 9 (15, 25,...,95), т.е. нечетное количество, их сумма закончится на 5.
Вывод: Сумма всех двузначных чисел закончится на 5
5
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
16.03.2017, 21:42
общий
это ответ
Здравствуйте, svrvsvrv!
Как вариант 10+11+...+54+55+...98+99=(10+99)+(11+98)+...+(54+55)=109*45. Очевидно, последняя цифра этого произведения =5
Как вариант 10+11+...+54+55+...98+99=(10+99)+(11+98)+...+(54+55)=109*45. Очевидно, последняя цифра этого произведения =5
5
Спасибо.
Об авторе:
Понеже не словес красных бог слушает, но дел наших хощет
Понеже не словес красных бог слушает, но дел наших хощет
16.03.2017, 21:45
общий
это ответ
Здравствуйте, svrvsvrv!
Возможно, менее изящный, но приемлемый способ решения поставленной задачи заключается в вычислении суммы арифметической прогрессии, которую образуют двузначные числа, то есть числа от
до 
Получается, что первый член прогрессии 
девяностый член прогрессии 
разность прогрессии 
сумма прогрессии
очевидно, заканчивается цифрой
Возможно, менее изящный, но приемлемый способ решения поставленной задачи заключается в вычислении суммы арифметической прогрессии, которую образуют двузначные числа, то есть числа от
до Получается, что первый член прогрессии девяностый член прогрессии разность прогрессии сумма прогрессииочевидно, заканчивается цифрой
5
Благодарю Вас.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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