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anjekawolf
@anjekawolf
July 2022
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Обчислити 1^2-2^2+3^2-4^2+...+99^2-100^2+101^2
У меня вопрос: если решать через арифметическую прогрессию, почему мы берем вторую формулу, а не первую?
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Verified answer
1^2-2^2+3^2-4^2+...+99^2-100^2+101^2=
1^2+(-2^2+3^2)+(-4^2+5^2)...+(-98^2+99^2)+(-100^2+101^2) =
1^2+(3-2)(3+2)+(5-4)(5+4)...+(99-98)(99+98)+(101-100)(101+100)=
1+5+9...+197+201=
a1=1; an=201; d=4; n=(201-1)/d+1=51
Sn=(1+201)*51/2 =
101*51=5151
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Answers & Comments
Verified answer
1^2-2^2+3^2-4^2+...+99^2-100^2+101^2=1^2+(-2^2+3^2)+(-4^2+5^2)...+(-98^2+99^2)+(-100^2+101^2) =
1^2+(3-2)(3+2)+(5-4)(5+4)...+(99-98)(99+98)+(101-100)(101+100)=
1+5+9...+197+201=
a1=1; an=201; d=4; n=(201-1)/d+1=51
Sn=(1+201)*51/2 = 101*51=5151