1.

How many consecutive natural numbers starting from 1 should be added to get 300?

Answer»

LET S=1+2+3+⋯+9=9×102=45

Next 10 to 19

⟹(1+0)+(1+1)+⋯(1+9)=1×10+S

Next 20 to 29

(2+0)+(2+1)+⋯(2+9)=2×10+S

⋮

So, 1 to 99

(1×10+2×10+⋯9×10)+10S

=10(1+2+3+⋯+9)+10S

=10S+10S=20S(1)

⋮

Similarly, for 100 to 199

10×10+10(1+2+3+⋯+9)+10S

=100+20S(2)

And for 200 to 300

200+20S+3(3)

So adding (1),(2),(3)

SUM of digits of numbers from 1 to 300

=60S+303=60×45+303

=3003


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