Binomial Theorem, Sequences and Series

Matching exercise

    
Match the items on the right to the items on the left.
Find the sum: 1 + 4/5 + 7/25 + 10/125 + ···
Find the sum of the first n terms of the series 1/(1+√2) + 1/(√2+√3) + 1/(√3+√4) + ...
If the product of the 4th, 5th and 6th terms of a geometric progression is 4096 and if
the product of the 5th, 6th and 7th-terms of it is 32768, find the sum of first 8 terms of the geometric progression.
If the 5th and 9th terms of a harmonic progression are 1/19 and 1/35 , find the 12th term of the sequence
35/16
√(n+1) − 1
255
1/47