TRONG QUYỂN NÂNG CAO PHÁT TRIỂN TOÁN 6 CÓ ĐẤY

Bạn lấy số cuối dãy trừ số đầu dãychia khoảng cách la 1 va tru 1 la tim ra so phan tu

Roi ban lay so dau day cong so cuoi daycong phan tu ban vua tinh ra chia 2

\(A=10\cdot11+11\cdot12+12\cdot13+...+29\cdot30\\ 3A=10\cdot11\cdot3+11\cdot12\cdot3+12\cdot13\cdot3+...+29\cdot30\cdot3\\ 3A=10\cdot11\cdot\left(12-9\right)+11\cdot12\cdot\left(13-10\right)+12\cdot13\cdot\left(14-11\right)+...+29\cdot30\cdot\left(31-28\right)\\ 3A=10\cdot11\cdot12-9\cdot10\cdot11+11\cdot12\cdot13-10\cdot11\cdot12+12\cdot13\cdot14-11\cdot12\cdot13+...+29\cdot30\cdot31-28\cdot29\cdot30\\ 3A=\left(10\cdot11\cdot12-10\cdot11\cdot12\right)+\left(11\cdot12\cdot13-11\cdot12\cdot13\right)+...+\left(28\cdot29\cdot30-28\cdot29\cdot30\right)+29\cdot30\cdot31-9\cdot10\cdot11\\ 3A=29\cdot30\cdot31-9\cdot10\cdot11\\ A=\dfrac{29\cdot30\cdot31-9\cdot10\cdot11}{3}\\ A=\dfrac{3\cdot\left(29\cdot10\cdot31-3\cdot10\cdot11\right)}{3}\\ A=29\cdot10\cdot31-3\cdot10\cdot11\\ A=10\cdot\left(29\cdot31-3\cdot11\right)\\ A=10\cdot866\\ A=8660\)

tổng này có:99-10+1=90 so hang

(10,10+99,99)x90:2=4954,05

k nhe

Lời giải:

$S=10.11+11.12+12.13+...+29.30$

$3S=10.11(12-9)+11.12(13-10)+12.13(14-11)+...+29.30(31-28)$

$=(10.11.12+11.12.13+12.13.14+...+29.30.31)-(9.10.11+10.11.12+...+28.29.30)$

$=29.30.31-9.10.11=25980$

$\Rightarrow S=8660$

\(A=10\cdot11+11\cdot12+12\cdot13+...+29\cdot30\)
\(\Leftrightarrow A=\left(1\cdot2+2\cdot3+3\cdot4+...+29\cdot30\right)-\left(1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\right)\)
\(\Leftrightarrow A=\frac{29\cdot30\cdot31}{3}-\frac{9\cdot10\cdot11}{3}\)
\(\Leftrightarrow A=29\cdot10\cdot31-3\cdot10\cdot11\)
\(\Leftrightarrow A=8990-330\)
\(\Leftrightarrow A=8660\)

\(B=1\cdot2\cdot3+2\cdot3\cdot4+...+49\cdot50\cdot51\)
\(\Leftrightarrow B=\frac{1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+49\cdot50\cdot51\cdot\left(52-48\right)}{4}\)
\(\Leftrightarrow B=\frac{1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+49\cdot50\cdot51\cdot52-48\cdot49\cdot50\cdot51}{4}\)
\(\Leftrightarrow B=\frac{49\cdot50\cdot51\cdot52}{4}\)
\(\Leftrightarrow B=49\cdot50\cdot51\cdot13\)
\(\Leftrightarrow B=1624350\)