[tex]a)21 + 42 + 63 + ... + 1890[/tex]
[tex] = 21(1 + 2 + 3 + ... + 90)[/tex]
[tex] = 21 \times \frac{90(90 + 1)}{2} [/tex]
[tex] = 21 \times \frac{90 \times 91}{2} [/tex]
[tex] = 21 \times 45 \times 91[/tex]
[tex] = 85995[/tex]
[tex]b)101 + 202 + 303 + ... + 909 + 1010 + ...9898 + 9999[/tex]
[tex] = 101(1 + 2 + 3 + ... + 9 + 10 + ... + 98 + 99)[/tex]
[tex] = 101 \times \frac{99(99 + 1)}{2} [/tex]
[tex] = 101 \times \frac{99 \times 100}{2} [/tex]
[tex] = 101 \times 99 \times 50[/tex]
[tex] = 499950[/tex]
[tex]Formul\check{a}\::\:1+2+3+...+n=\frac{n(n+1)}{2}[/tex]
