Prove the theorem below using the techniques ofbinding the term and splitting thesumorapproximation by integralsto find a tight bound for the sum. Make sure yourproof is complete, concise, clear and precise. Theorem 4.n∑i=1id∈Θ(nd+1)(5 points) 2.Prove the theorem below using the techniques ofbinding the term and splitting thesumorapproximation by integralsto find a tight bound for the sum. Make sure yourproof is complete, concise, clear and precise. Theorem 5.n∑i=1(log2i)c∈Θ(n(log2n)c)(10 points) 3. Consider the recurrenceT(n).T(n)={cifn≤12T(⌊n4⌋) +16ifn>1a)Use the recursion tree or repeated substitution method to come up with a goodguess for a boundf(n) on the recurrenceT(n).b) State and prove by induction two theorems showingT(n)∈Θ(f(n)).GradingYou will be docked points for errors in your math, disorganization, unclarity, orincomplete proofs