Question-153905

Question Number 153905 by liberty last updated on 12/Sep/21

Commented by MJS_new last updated on 12/Sep/21

3^{3} (\frac{1}{2 \times 5} + \frac{1}{(2 + 3) (5 + 3)} + \frac{1}{(2 + 2 \times 3) (5 + 2 \times 3)} + \dots + \frac{1}{(2 + 11 \times 3) (5 + 11 \times 3)})

Answered by MJS_new last updated on 12/Sep/21

\frac{81}{19}

Commented by liberty last updated on 12/Sep/21

h o w ?

Answered by som(math1967) last updated on 12/Sep/21

A = 3^{2} (\frac{3}{2 \times 5} + \frac{3}{5 \times 8} + \frac{3}{8 \times 11} \dots + \frac{3}{35 \times 38})

= 3^{2} (\frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{11} + \dots \frac{1}{35} - \frac{1}{38}]

= 3^{2} \times (\frac{1}{2} - \frac{1}{38}) = 9 \times \frac{18}{38} = \frac{81}{19}

Commented by liberty last updated on 12/Sep/21

w o n d e r f u l l

Commented by puissant last updated on 12/Sep/21

Wow what a look ��