Tính tổng H = 1.99 + 2.98 + 3.97 + … + 50.50

2 bình luận về “Tính tổng H = 1.99 + 2.98 + 3.97 + … + 50.50”

1. Tính tổng $H=1.99+2.98+3.97+\dots +50.50$

   $=$ $H=1.(100-1)+2.(100-2)+3.(100-3)+\dots +50.(100-50)$

   $=$ $H=100.(1+2+3+\dots +50)-$ $($ $1^2$ $+$ $2^2$ $+$ $3^2$ $+\dots$ ${50}^2$ $)$

   $=$ $100.1275–$ {$1.(2-1)+2.(3-1)+3.(4-1)+\dots +50.(51-1)$ }

   $=$ $127500–[(1.2+2.3+3.4+\dots +50.51)-(1+2+3+\dots +50)]$ 

   $=$ $127500-$ ${\displaystyle \frac{1.2.3-1.2.3+2.3.4-\dots -49.50.51+50.51.52}{3}}$ $-1257$ 

   $=$ $127500–44200-1257$ 

   $=$ $84575$ 

   Chúc bn hc tốt!~

   Trả lời
2. H = 1 . 99 + 2 . 98 + 3 . 97 + ….. + 50 . 50

   = 1 . (100 – 1) + 2 . (100 − 2) + 3 . (100 − 3)+ ……. + 50(100 − 50)

   = 100 . (1 + 2 + 3 + …… + 50) − (1^{2} + 2^{2} + 3^{2} + …… 50^{2})

   = 100 . 1275 – [1 . (2 – 1) + 2 . (3 – 1) + 3 . (4 – 1) + …… + 50 . (51 – 1)]

   = 127500 – [(1 . 2 + 2 . 3 + 3 . 4 + …… + 50 . 51) – (1 + 2 + 3 + …… + 50)] 

   = 127500 – (1 . 2 . 3 – 1 . 2 . 3 + 2 . 3 . 4 – …… – 49 . 50 . 51 + 50 . 51 . 52)/3 – 1257

   = 127500 – 44200 – 1257

   = 84575 

   Trả lời