1. Consider a sequence where the $$n^{th}$$ term, $$t_n = n/(n+2), n =1, 2, ....$$ The value of $$t_3 * t_4 * t_5 * …..* t_{53}$$ equals.
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By: anil on 05 May 2019 02.29 am
substituting 3,4...53 in the given function, we get
$$t_3 = frac{3}{5}$$
$$t_4 = frac{4}{6}$$
$$t_5 = frac{5}{7}$$
$$t_6 = frac{6}{8}$$
Multiplying the values, we get $$frac{3}{5}*frac{4}{6}*frac{5}{7}*....frac{52}{54}*frac{53}{55} $$ which ultimately after cancellations give $$frac{3*4}{54*55}=frac{2}{495}$$
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$$t_3 = frac{3}{5}$$
$$t_4 = frac{4}{6}$$
$$t_5 = frac{5}{7}$$
$$t_6 = frac{6}{8}$$
Multiplying the values, we get $$frac{3}{5}*frac{4}{6}*frac{5}{7}*....frac{52}{54}*frac{53}{55} $$ which ultimately after cancellations give $$frac{3*4}{54*55}=frac{2}{495}$$