What is the sum of the first 15 terms of the series 1/{6\times7}+1/{7\times8}+1/{8\times9}+...?

Decimals and Fractions Practice Test 3

Question : 28 of 40

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What is the sum of the first 15 terms of the series

1/{6×7}+1/{7×8}+1/{8×9}+...?

Solution:

Sum of the first 15 terms

=1/{6×7}+1/{7×8}+1/{8×9}+...+1/{20×21}

=1/6-1/7+1/7-1/8+1/8-1/9...... 1/20-1/21

=1/6-1/21=0.11

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