Find the general form of the solution to a linear homogeneous recurrence relation with constant coefficients for which the characteristic roots are 4, -2 and 3 with multiplicities 2, 1 and 3, respectively. The relation also has a non-homogeneous part which is a linear combination of 3n and 4n.
A linear recurrence relation with constant coefficients is solved by combining the solution of its associated homogeneous relation with a particular solution of the non-homogeneous part. The homogeneous solution is obtained from the characteristic equation, whose roots determine the structure of the general term. When a characteristic root (r) has ___ _____ __________ _____ _____ _________ _________ ________ ____ ________ _______.
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यदि पुनरावृत्ति संबंध का हल
है , तो
और f(n) के मान ज्ञात कीजिए।
Use generating function to prove the identity
If the solution of the recurrence relation is
, then determine the values of
and f(n).
विलय शाटन कलन-विधि की काल जटिलता ज्ञात कीजिए।
Compute the time complexity of the merge sort algorithm.
A bank pays you interest per year. In addition, you receive Rs. 100 as bonus at the end of the year (after the interest is paid). Find a recurrence for the amount of money after n years if you invest Rs. 2000.
निम्नलिखित में से प्रत्येक कथन का विलोम लिखिए:
i) यदि p एक अभाज्य संख्या है, और a और b दो प्राकृतिक संख्याएँ हैं, और p, a या b को विभाजित करता है , तो p, ab को विभाजित करता है।
ii) एक त्रिभुज में, यदि
है, तो
होगा।