tinh
a) 2+22+222+2222+…+222…2(50c/s 2)
b)B= $\frac{1}{1.2.3}$ + $\frac{1}{2.3.4}$ +…+ $\frac{1}{97.98.99}$ + $\frac{1}{98.99.100}$
lam chi tiet
tinh a) 2+22+222+2222+…+222…2(50c/s 2) b)B= $\frac{1}{1.2.3}$ + $\frac{1}{2.3.4}$ +…+ $\frac{1}{97.98.99}$ + $\frac{1}{98.99.100}$ lam chi tie
By Aaliyah
a,=2.(1+11+111+………..+111…11(50))
=2.(9+99+999+……+.999…..9999(50)/9
=2.(10-1+10^2-1+………………..+10^50-1)/9
=2.((1+10+10^2+….+10^50−1)−17/9
=2. (10^51-1/9)-18/9
B=1/1.2.3+1/2.3.4+………….+1/97.98.99+1/98.99.100
2B=2/1.2.3+2/2.3.4+………….+2/98.99.100
2B=1/1.2-1/2.3+1/2.3-1/3.4+………………..+1/98.99-1/99.100
2B=1/1.2-(1/2.3-1/2.3)-…………………………-(1/98.99-1/98.99)-1/99.100
2B=1/1.2-0-0-0-0-……..-0-1/99.100=1/1.2-1/99.100
2B=1/2-1/9900=4950/9900-1/9900=4949/9900
B=4949/9900 .1/2=4949/19800
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