SOLUTION: Prove that 0,3 < S < 0,4 S= 1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(2014*2017)

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Question 1023304: Prove that 0,3 < S < 0,4
S= 1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(2014*2017)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
S = %281%2F3%29%281-1%2F4%29%2B%281%2F3%29%281%2F4-1%2F7%29%2B%281%2F3%29%281%2F7-1%2F10%29+...+ %281%2F3%29%281%2F2011-1%2F2014%29+%2B+%281%2F3%29%281%2F2014-1%2F2017%29
=%281%2F3%29*(1+-+1%2F4+%2B+1%2F4+-+1%2F7+%2B+1%2F7+-+1%2F10+...+ 1%2F2011-1%2F2014+%2B+1%2F2014-1%2F2017)
=%281%2F3%29%281-1%2F2017%29 = S
But S=+%281%2F3%29%282016%2F2017%29+=+672%2F2017+= 0.333168... >0.3, and also
S+=+%281%2F3%29%282016%2F2017%29+%3C+1%2F3+=+0.33333....< 0.4
Hence,
0.3 < S < 0.4.