( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750

( x + x + ... + x ) + ( 1 + 2 + ... + 100 ) = 5750

SSH là : ( 100 - 1) : 1 + 1 = 100 ( số )

Tổng là : ( 100 + 1 ) . 100 : 2 = 5050

=> 100x + 5050 = 5750

=> 100x = 700

=> x = 7

Vậy x = 7

các bạn ơi nhanh lên mình k cho

(x + 1) + (x + 2) + (x + 3) + .... + (x + 100) = 5750
=> 100x + (1 + 2 + 3 + ... + 100) = 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7

HỌC TỐT

(x + 1) + (x + 2) + (x + 3) + .... + (x + 100) = 5750

=> 100x + (1 + 2 + 3 + ... + 100) = 5750

=> 100x + 5050 = 5750

=> 100x = 5750 - 5050

=> 100x = 700

=> x = 700 : 100

=> x = 7 

chúc hok tốt!!! ^_^

Lê Phúc Đạt:

(x + 1) + (x + 2) +...+ (x + 100) = 5750

Đặt: (x + 1) + (x + 2) +...+ (x + 100) = S

Từ 1 đến 100 có 100 số hạng:

=> S = 100x + (1 + 2 +...+100)

     S = 100x + (100 + 1). 100 : 2

     S = 100x + 5050

=> 100x + 5050 = 5750

      100x             = 5750 - 5050

      100x             = 700

            x              = 700 : 100

            x              = 7

Vậy x = 7

Tham khảo nha!

ta có: (x+1)+(x+2)+(x+3)+....+(x+100)=5750

        =(x + x+ x+....+ x)+(1+2+3+....+100)=5750

    suy ra có 100x và 100 so hang

      =100x + 5050=5750

=100x=5750-5050

=100x=700

=x=700 : 100

=x=7

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+50\right)=1325\)

\(\Leftrightarrow50x+\left(1+2+3+...+50\right)=1325\)

\(\Leftrightarrow50x+\frac{50.\left(50+1\right)}{2}=1325\)

\(\Leftrightarrow50x+1275=1325\)

\(\Leftrightarrow50x=50\)

\(\Leftrightarrow x=1\)

Vậy x =1

Tính tổng: 1 + 2+ 3 +... +50 = (50 + 1).50 : 2 = 1275

( x +1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 50 )  = 1325 

( chú ý vế trái của 50 hạng tử )

( x + x + x +... + x ) + ( 1+ 2 + 3 +...+ 50 ) =1325

50 . x + 1275 =1325

50 . x  = 1325 - 1275

50 . x = 50

x = 1

pt \(\Leftrightarrow\left(\frac{x-2}{27}-1\right)+\left(\frac{x-3}{26}-1\right)+\left(\frac{x-4}{25}-1\right)+\left(\frac{x-5}{24}-1\right)+\left(\frac{x-44}{5}+3\right)=0\)

\(\Leftrightarrow\frac{x-29}{27}+\frac{x-29}{26}+\frac{x-29}{25}+\frac{x-29}{24}+\frac{x-29}{5}=0\)

\(\Leftrightarrow\left(x-29\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\right)=0\)

Mà \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\ne0\)

\(\Rightarrow x-29=0\Leftrightarrow x=29\)

\(\Rightarrow\)\(\frac{2}{6}\)+ \(\frac{2}{12}\)+ \(\frac{2}{20}\)+...+\(\frac{2}{x\left(x+1\right)}\)= \(\frac{2011}{2013}\)

\(\Rightarrow\)\(\frac{2}{2.3}\)+ \(\frac{2}{3.4}\)+ \(\frac{2}{4.5}\)+...+  \(\frac{2}{x\left(x+1\right)}\)= \(\frac{2011}{2013}\)

\(\Rightarrow\)\(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)+...+ \(\frac{1}{x}\)- \(\frac{1}{x+1}\)= \(\frac{2011}{2013}\): 2

\(\Rightarrow\)\(\frac{1}{2}\)- \(\frac{1}{x+1}\)=  \(\frac{2011}{4026}\)

\(\Rightarrow\)\(\frac{1}{x+1}\)= \(\frac{1}{2}\)- \(\frac{2011}{4026}\)= \(\frac{1}{2013}\)

\(\Rightarrow\)\(x+1=2013\)

Bạn tự làm tiếp nha !