Question
Given A = 265 and B = (264 + 263 + 262 + ..... +20), which of the following is true?
Answer: Option D
B is in G.P. with a = 20, r = 2, n = 65
$$\eqalign{
& \therefore {S_n} = \frac{{a\left( {{r^n} - 1} \right)}}{{r - 1}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{2^0}\left( {{2^{65}} - 1} \right)}}{{2 - 1}} \cr
& \therefore B = {2^{65}} - 1 \cr
& \Rightarrow B = A - 1 \cr
& \therefore A\,{\text{is}}\,{\text{larger}}\,{\text{then}}\,B\,{\text{by}}\,1 \cr} $$
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B is in G.P. with a = 20, r = 2, n = 65
$$\eqalign{
& \therefore {S_n} = \frac{{a\left( {{r^n} - 1} \right)}}{{r - 1}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{2^0}\left( {{2^{65}} - 1} \right)}}{{2 - 1}} \cr
& \therefore B = {2^{65}} - 1 \cr
& \Rightarrow B = A - 1 \cr
& \therefore A\,{\text{is}}\,{\text{larger}}\,{\text{then}}\,B\,{\text{by}}\,1 \cr} $$
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