Question

find the sum of 1/1×2+1/2×3+1/3×4+..............1/10×11​

Answer 1

Answer:

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Step-by-step explanation:

Denominator of all terms formed by multiplication of three terms ,of which difference of first and third is 2 .

1st term = 1/1*2*3 =1/2(1/1*2 – 1/2*3)

2nd term=1/2*3*4=1/2(1/2*3 - 1/3*4)

3rd term=1/3*4*5=1/2(1/3*4 - 1/4*5 )

10th term=1/10*11*12=1/2( 1/10*11 - 1/11*12)

adding all the terms

S = 1/2(1/1*2 - 1/11*12)

=1/2(1/2 - 1/132 )

=1/2(65/132)

= 65/264 ans