Tom , I might be able to help you with OG response (the response , I must say , may be difficult to understand initally but it has an important takeaway in it ) "is Z* not Equal to 0" makes your question a lil diff from OG questions. So we are looking for this Z* function not being equal ...
bhdeepak, i am going to give it a try x = (-1) n = 14 ( 2 + 3 + 4 + 5) the equation reduces to Sum = 1 -1 +(-1)^14 + (-1)^15 +....x^(n+n)+x^(2n+1).... Sum = 1-1+1-1+......+(-1)^2n + (-1)^2n+1..... Sum = 0 if the exponent in last number of the sequence is odd and will be 1 if the exponent in last num...
I believe both "that contains" and "containing" have the same relevance in these examples. Only one is introducing a relative clause (that .....) , other is a present participial phrase (containing ...) / In fact you can convert a relative clause into a present participial phrase...
Based on my understanding so far and applying lil foresight , I modestly claim that the answer to your question is "No, there can be no instance where the exact answer varies from statement 1 to statement 2" [editor: you are correct in spirit, but note that this actually means that the ans...
in a series of three consecutive integers, one of them has to be a multiple of 3. the error you made was not to consider zero as a multiple of 3. "Zero is a multiple of every number" (simply put , to be a multiple , the number should leave a remainder of 0 when divided by 3 and Zero does t...
you can align them to combine then a < b b < c => a < b < c but you cannot add them the way you did after aligning them. the correct way is - a < b b< c a+b < c +b and NOT a < 2b < c ( just take a = 1 , b = 2 , c = 3 and you will see the mistake you made ) The answer to...
Consider this : The weight of the decrease in C(13%) will tilt the scale towards negative side , so you need more weight on P(8%) to be able to balance it closer to it (+1%) ................................+1 -|-----------------|--|-------|----------- -13......................0.............8 Where d...
couple of ways n divided by 9 leaves remainder 6. 7n will leave the same remainder as 7*(remainder of n when divided by 9) = 7*6/ 9 = 42/9 = 6 alternate way to understand the above. 7 and 9 and prime to each other , in other words , they dont have any common factor. so 7 divided by 9 will leave rema...
while we wait for Ron to answer your question ,I will try to answer a part of your question (though not absolutely ) absolute phrases - act as adverbs / often show cause and effect , may contain other verbs BUT will not contain a helping verb as part of its core. Taking the example you cited - The c...
I believe it should be relevant since they have specifically given the sequence of how the points are laid out in number line ..... I think the question, keeping the assumption you bring forth , would be: [In the above figure] - deleted , Points A, B, C, D, and E lie on a line. A is on both circles,...
will give a crack at the question the correct answer choice must be 100% provable convergence : two classes with different traits ,are/put in same eniv, will adapt exclusive of each other and acquire some external features (e.g. i-saurs and fish - both had fins / but belonged to diff class ) (A) The...