Permutations And Combinations

Question
CBSEENMA11013049

which term of the series:

space space 1 minus 1 half plus 1 fourth minus 1 over 8 plus........ space is space minus 1 over 128

Solution

The given series is: space space space 1 minus 1 half plus 1 fourth minus 1 over 8 plus......
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#6 {main}</pre>
Let fraction numerator negative 1 over denominator 128 end fraction be the nth term

∴                            straight t subscript straight n equals space fraction numerator negative 1 over denominator 128 end fraction
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#6 {main}</pre>      or      1 open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses to the power of straight n minus 1 end exponent space equals space minus 1 over 2 to the power of 7  or   open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses to the power of straight n minus 1 end exponent space equals space open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses to the power of 7
or                           n - 1 = 7              or n= 8

∴    fraction numerator negative 1 over denominator 128 end fraction  is the 8th term.

Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.