Find the sum of the following series 1/14+ 1/47+1/710+1/1013+ 1/13*16

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Answer: 5/16

1/1*4+ 1/4*7+1/7*10+1/10*13+ 1/13*16

= 1/3[3/1*4+ 3/4*7+3/7*10+3/10*13+ 3/13*16]

=13(1 – 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + 1/10 – 1/13 + 1/13 – 1/16 )

= 1/3(1 – 1/16)

= 1/3(15/16)

= 5/16

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Find the sum of the following series 1/1*4+ 1/4*7+1/7*10+1/10*13+ 1/13*16