Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
-8
37778
1
avatar+54 

1.) 

The first term of a sequence is 2, and each subsequent term is the reciprocal of the square of the preceding term. What is the positive square root of the fifth term?

 

2.)

Calculate

(112)(113)(114)(112009).

 

3.)

What is the maximum number of consecutive positive integers that can be added together to create a sum less than 400?

 

4.)

What is the units digit of $2^{1993} + 3^{1993}$?

 

5.)

What is the value of the sum 

$\dfrac {1}{1\cdot 3} + \dfrac {1}{3\cdot 5} + \dfrac {1}{5\cdot 7} + \dfrac {1}{7\cdot 9} + \cdots + \dfrac {1}{199\cdot 201}$

? Express your answer as a fraction in simplest form.

 

6.)

Compute

112+214+318++n12n+.

 Jan 27, 2018
edited by Jdaye  Jan 28, 2018
 #1
avatar
+3

1)

 

2, 1/4, 16, 1/256, 65,536........etc.

Sqrt(65,536) = 256

 

3)

[a*(a+1)] / 2 =400, solve for a

a = ~ 27, so that:

1+2+3+.........+27 = 378

 

4)

2^1993 + 3^1993 =2^1 + 3^1 =5 - last digit !!.

 Jan 27, 2018

1 Online Users