tiny-tim said:Hi S.R.!
Hint: each term is 1/√n√n+1(√n + √n+1) …
but what is 1/(√n + √n+1) ?
S.R said:
Infinitum said:
S.R said:
Infinitum said:Yep! Now, what did you do next?
Edit : maybe its just too simple from here
S.R said:
S.R said:
S.R said:
Its better to use different term letters for it. So, what do you get from that relation, by summing it all up?S.R said:
tiny-tim said:
.S.R said:
Infinitum said:Its wrong
[tex]Tn = \frac{\sqrt{n+1} - \sqrt{n}}{\sqrt{n}\sqrt{n+1}}[/tex]
Give it another go, and write out the answer
S.R said:
I don't notice any patterns to find the sum?Infinitum said:
S.R said:
micromass said:
S.R said:
tiny-tim said:what is [tex]\Sigma_5^{21}\ \left(\frac{1}{n}-\frac{1}{n+1}\right)[/tex] ?
S.R said:
tiny-tim said:
The first step in solving a summation of a sequence is to identify the pattern or formula of the sequence. This can be done by examining the numbers in the sequence and looking for any relationships or repeating patterns. Once the pattern is identified, you can use it to generate the terms of the sequence and simplify the summation.
There are several methods for solving a summation of a sequence, including the direct method, the difference method, and the substitution method. The direct method involves plugging in the values of each term in the sequence and adding them together. The difference method involves subtracting two consecutive terms to simplify the summation. The substitution method involves replacing the summation with an equivalent expression that is easier to solve.
The upper and lower limits of a summation can be determined by looking at the given sequence and identifying the starting and ending values. The lower limit is usually the first term in the sequence, while the upper limit is the last term. If the sequence is given in terms of a variable, the limits can also be determined by the range of values for that variable.
Yes, you can use a calculator to solve a summation of a sequence. However, it is important to know how to solve it manually as well. Some calculators have specific functions for summations, while others may require you to input the formula or pattern of the sequence. Additionally, make sure to check your calculator's settings to ensure that it is calculating the summation correctly.
If you are having trouble solving a summation of a sequence, try breaking it down into smaller parts. Look for patterns in the sequence and try to simplify the summation using different methods. You can also ask for help from your teacher, classmates, or a tutor. Additionally, there are many online resources and tutorials available that can provide step-by-step guidance on how to solve different types of summations.