Quick Quiz on Sequence & Series

What is the sum of ‘n’ terms in the series:?

Consider a sequence then n^th term t_n = n/(n + 2), n = 1, 2… the value of t₃ x t₄ x t₅ x …… x t₅₃ equals:

If and then a₁₀₀ is equal to:

Let u_n+1 = 2u_n + 1; (n=0, 1, 2, ...) and u₀ = 0. Then u₁₀ nearest to

For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference of squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?