\(Tính:1+\dfrac{1+2}{2}+\dfrac{1+2+3}{3}+...+\dfrac{1+2+...+100}{100}\)
S1=1+2+3+...+999
S2=10+12+14+...+2018
S3=1+2+22+23+...+210
S4=1+3+32+33+34+...+3100
S5=(-1)+5+(-9)+13+...+(-41)+45
Bài 2 : Thực hiện phép tính nhanh nếu có thể :
l) -2019 . 2020 + 1010 . 38
m) 1 - 2 - 3 - 4 + 5 - 6 - 7 - 8 + 9 - 10 - 11 - 12 + ..... + 97 - 98 - 99 -100.
o) 5^1 + 5^2 + 5^3 + .... + 5^199 + 5^200.
p) 3^0 - 3^2 + 3^3 - 3^4 +..... + 3^2017 - 3^2018 + 3^2019 -3^2020.
q) 6 + 6.9 + 6.9^2 + 6.9^3 + ....+ 6.9^99.
r) (-1) . (-1)^2 . (-1)^3 . (-1)^4 .... (-1)^99 . (-1)^100
cmr
100-(1+1/2+1/3+...+1/100)=1/2+2/3+3/4+....+99/100
Cho A = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + ... + 99 . 100 . Biết C = A + 10 . 11 . Tính C .
1)tính
2^100-(1+2+2^2+2^3+....+2^100)
Tính : \(A=-\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}-\dfrac{1}{3^{101}}\)
tinh
A=1/1+2+1/1+2+3+1/1+2+3+4+...................+1/1+2+3+4+...............+100
1: Tính B
\(B=1+\dfrac{1}{2}\cdot\left(1+2\right)+\dfrac{1}{3}\cdot\left(1+2+3\right)+\dfrac{1}{4}\cdot\left(1+2+3+4\right)+...+\dfrac{1}{100}\cdot\left(1+2+3+...+100\right)\)