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...

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...

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.

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

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.

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)

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

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,...

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)

(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...

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...

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

The serie 2/[(n+2)(n-1)] (n starting from 3 until infinite)

Does the sum changes in this case and does the limit change too?