Question

which term of 2-1/√2+1/4+...is 1/32
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Answer 1

Step-by-step explanation:

$2 - \frac{1}{ \sqrt{2} } + \frac{1}{4} + .... = \frac{1}{32} \\ \frac{ - 1}{ \sqrt{2} } + \frac{1}{4} + ....= \frac{1}{32} - 2 \\ \frac{ - 1}{ \sqrt{2} } + \frac{1}{4} + ....= \frac{ - 63}{32} \\ \frac{ - 1}{ \sqrt{2} } + .... = \frac{ - 63}{32} - \frac{1}{4} \\ \frac{ - 1}{ \sqrt{2} } + ....= \frac{ - 63}{32} - \frac{8}{32} \\ \frac{ - 1}{ \sqrt{2} } + ....= \frac{ - 71}{32} \\ ...... = \frac{ - 71}{32} + \frac{1}{ \sqrt{2} } \\ ...... = \frac{ - 70}{32} + \frac{16 \sqrt{2} }{32} \\ ...... = \frac{ - 70 + 16 \sqrt{2} }{32} \\ = \frac{2( - 35 + 8 \sqrt{2}) }{32} = \frac{ - 35 + 8 \sqrt{2} }{16}$

Thanks for the question bro