pls clear my confusion

pls clear my confusion

FORMULAE FOR SERIES +N/2+N/4+N/8......1

Can anyone explain how you prove a general term is true for a series, un+1=un/1+un u1=2 (i) find u2 and u3 (ii) Hence suggest an expression for un and so I have found...

∞∑n=1 (x−4)^n /n^n

1,3,7,?,121,721

A. summation of negative forty five times n from n equals zero to fifteen B. summation of the quantity negative nine plus five n from n equals zero to fifteen C. summation of the quantity...

abbcccddddeeeee........... what will be the 126th digit?

Determine whether the sequence is increasing, decreasing, or not monotonic. an = 1/(6n+7) Is the sequence bounded? Yes or No? Explain.

Determine whether the sequence is increasing, decreasing, or not monotonic. an = 4n(−7)n Is the sequence bounded? Yes or No? Explain.

I have a series (Un)n∈Ν. U0=2 and Un+1=1/4(Un)+1. I need to find a series (Vn)n∈Ν and a∈R such that Vn=Un+a and that (Vn) is geometric.

A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce it rises vertically to 2/3 the height from which it fell. (i)...

The first 3 terms of a geometric expression are x, 10 − x ,and 2x + 1 where x > 0. Find the value of the common ratio, r.

Sum to n terms of series 1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 +.......

I don't understand how to find the sum if I don't know what term the last one (252)? How would I determine which term this is (t of ?=252)

Hello, could you help me find the formula for this series, please? How do I go about it? 4,9,16,25,...I know it starts with adding 5 and adding 2 more with every number, so adding 7 next,...

(a) Starting with the first term, find the least number of terms that have a sum greater than 1500 (b) Starting with the first term, find also the number of terms that have a sum of...

If tn= (n+2)(n+3)/4 for n=1,2,3..... Then find the sum of 1/t1 + 1/t2 + 1/t3.... 1/t2003

The value of 2^1/4 * 4^1/8 * 8^1/16 *16^1/32...... Till infinity Is. (The answer is 2)

Please help me to find sum of this unlimeted serie: 1+2+3+5/7+3/2+4/3+25/49+3+4+... Thanks in advice

This is a multiple choice question A. Converges by the Ratio Test B. Diverges by the Ratio Test C. The Ratio Test is inconclusive Please...