Book Maths Puzzle Numerical Ability

T_(k+1)/T_k
how do we simplify this ratio pls help. thanks in advance

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Book Other Question

1/2+√5 + 1/√5+√6 + 1/√6+√7 +1/√7+√8 +1/√8+3 is the operation * is applied to a number gives as its result 10 subtract from twice the number. what is *(*9)?